{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Table of Contents](./table_of_contents.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Probabilities, Gaussians, and Bayes' Theorem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import division, print_function\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <style>\n",
       "        .output_wrapper, .output {\n",
       "            height:auto !important;\n",
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       "        }\n",
       "        .output_scroll {\n",
       "            box-shadow:none !important;\n",
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     "execution_count": 2,
     "metadata": {},
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   ],
   "source": [
    "#format the book\n",
    "import book_format\n",
    "book_format.set_style()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "The last chapter ended by discussing some of the drawbacks of the Discrete Bayesian filter. For many tracking and filtering problems our desire is to have a filter that is *unimodal* and *continuous*. That is, we want to model our system using floating point math (continuous) and to have only one belief represented (unimodal). For example, we want to say an aircraft is at (12.34, -95.54, 2389.5) where that is latitude, longitude, and altitude. We do not want our filter to tell us \"it might be at (1.65, -78.01, 2100.45) or it might be at (34.36, -98.23, 2543.79).\" That doesn't match our physical intuition of how the world works, and as we discussed, it can be prohibitively expensive to compute the multimodal case. And, of course, multiple position estimates makes navigating impossible.\n",
    "\n",
    "We desire a unimodal, continuous way to represent probabilities that models how the real world works, and that is computationally efficient to calculate. Gaussian distributions provide all of these features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mean, Variance, and Standard Deviations\n",
    "\n",
    "Most of you will have had exposure to statistics, but allow me to cover this material anyway. I ask that you read the material even if you are sure you know it well. I ask for two reasons. First, I want to be sure that we are using terms in the same way. Second, I strive to form an intuitive understanding of statistics that will serve you well in later chapters. It's easy to go through a stats course and only remember the formulas and calculations, and perhaps be fuzzy on the implications of what you have learned.\n",
    "\n",
    "### Random Variables\n",
    "\n",
    "Each time you roll a die the *outcome* will be between 1 and 6. If we rolled a fair die a million times we'd expect to get a one 1/6 of the time. Thus we say the *probability*, or *odds* of the outcome 1 is 1/6. Likewise, if I asked you the chance of 1 being the result of the next roll you'd reply 1/6.  \n",
    "\n",
    "This combination of values and associated probabilities is called a [*random variable*](https://en.wikipedia.org/wiki/Random_variable). Here *random* does not mean the process is nondeterministic, only that we lack information about the outcome. The result of a die toss is deterministic, but we lack enough information to compute the result. We don't know what will happen, except probabilistically.\n",
    "\n",
    "While we are defining terms, the range of values is called the [*sample space*](https://en.wikipedia.org/wiki/Sample_space). For a die the sample space is {1, 2, 3, 4, 5, 6}. For a coin the sample space is {H, T}. *Space* is a mathematical term which means a set with structure. The sample space for the die is a subset of the natural numbers in the range of 1 to 6.\n",
    "\n",
    "Another example of a random variable is the heights of students in a university. Here the sample space is a range of values in the real numbers between two limits defined by biology.\n",
    "\n",
    "Random variables such as coin tosses and die rolls are *discrete random variables*. This means their sample space is represented by either a finite number of values or a countably infinite number of values such as the natural numbers. Heights of humans are called *continuous random variables* since they can take on any real value between two limits.\n",
    "\n",
    "Do not confuse the *measurement* of the random variable with the actual value. If we can only measure the height of a person to 0.1 meters we would only record values from 0.1, 0.2, 0.3...2.7, yielding 27 discrete choices. Nonetheless a person's height can vary between any arbitrary real value between those ranges, and so height is a continuous random variable. \n",
    "\n",
    "In statistics capital letters are used for random variables, usually from the latter half of the alphabet. So, we might say that $X$ is the random variable representing the die toss, or $Y$ are the heights of the students in the freshmen poetry class. Later chapters use linear algebra to solve these problems, and so there we will follow the convention of using  lower case for vectors, and upper case for matrices. Unfortunately these conventions clash, and you will have to determine which an author is using from context. I always use bold symbols for vectors and matrices, which helps distinguish between the two."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probability Distribution\n",
    "\n",
    "\n",
    "The [*probability distribution*](https://en.wikipedia.org/wiki/Probability_distribution) gives the probability for the random variable to take any value in a sample space. For example, for a fair six sided die we might say:\n",
    "\n",
    "|Value|Probability|\n",
    "|-----|-----------|\n",
    "|1|1/6|\n",
    "|2|1/6|\n",
    "|3|1/6|\n",
    "|4|1/6|\n",
    "|5|1/6|\n",
    "|6|1/6|\n",
    "\n",
    "We denote this distribution with a lower case p: $p(x)$. Using ordinary function notation, we would write:\n",
    "\n",
    "$$P(X{=}4) = p(4) = \\frac{1}{6}$$\n",
    "\n",
    "This states that the probability of the die landing on 4 is $\\frac{1}{6}$. $P(X{=}x_k)$ is notation for \"the probability of $X$ being $x_k$\". Note the subtle notational difference. The capital $P$ denotes the probability of a single event, and the lower case $p$ is the probability distribution function. This can lead you astray if you are not observent. Some texts use $Pr$ instead of $P$ to ameliorate this. \n",
    "\n",
    "Another example is a fair coin. It has the sample space {H, T}. The coin is fair, so the probability for heads (H) is 50%, and the probability for tails (T) is 50%. We write this as\n",
    "\n",
    "$$\\begin{gathered}P(X{=}H) = 0.5\\\\P(X{=}T)=0.5\\end{gathered}$$\n",
    "\n",
    "Sample spaces are not unique. One sample space for a die is {1, 2, 3, 4, 5, 6}. Another valid sample space would be {even, odd}. Another might be {dots in all corners, not dots in all corners}. A sample space is valid so long as it covers all possibilities, and any single event is described by only one element.  {even, 1, 3, 4, 5} is not a valid sample space for a die since a value of 4 is matched both by 'even' and '4'.\n",
    "\n",
    "The probabilities for all values of a *discrete random value* is known as the *discrete probability distribution* and the probabilities for all values of a *continuous random value* is known as the *continuous probability distribution*.\n",
    "\n",
    "To be a probability distribution the probability of each value $x_i$ must be $x_i \\ge 0$, since no probability can be less than zero. Secondly, the sum of the probabilities for all values must equal one. This should be intuitively clear for a coin toss: if the odds of getting heads is 70%, then the odds of getting tails must be 30%. We formulize this requirement as\n",
    "\n",
    "$$\\sum\\limits_u P(X{=}u)= 1$$\n",
    "\n",
    "for discrete distributions, and as \n",
    "\n",
    "$$\\int\\limits_u P(X{=}u) \\,du= 1$$\n",
    "\n",
    "for continuous distributions.\n",
    "\n",
    "In the previous chapter we used probability distributions to estimate the position of a dog in a hallway. For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sum =  1.0\n"
     ]
    },
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d9166773c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import kf_book.book_plots as book_plots\n",
    "\n",
    "belief = np.array([1, 4, 2, 0, 8, 2, 2, 35, 4, 3, 2])\n",
    "belief = belief / np.sum(belief)\n",
    "with book_plots.figsize(y=2):\n",
    "    book_plots.bar_plot(belief)\n",
    "print('sum = ', np.sum(belief))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each position has a probability between 0 and 1, and the sum of all equals one, so this makes it a probability distribution. Each probability is discrete, so we can more precisely call this a discrete probability distribution. In practice we leave out the terms discrete and continuous unless we have a particular reason to make that distinction."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Mean, Median, and Mode of a Random Variable\n",
    "\n",
    "Given a set of data we often want to know a representative or average value for that set. There are many measures for this, and the concept is called a [*measure of central tendency*](https://en.wikipedia.org/wiki/Central_tendency). For example we might want to know the *average* height of the students in a class. We all know how to find the average of a set of data, but let me belabor the point so I can introduce more formal notation and terminology. Another word for average is the *mean*. We compute the mean by summing the values and dividing by the number of values. If the heights of the students in meters is \n",
    "\n",
    "$$X = \\{1.8, 2.0, 1.7, 1.9, 1.6\\}$$\n",
    "\n",
    "we compute the mean as\n",
    "\n",
    "$$\\mu = \\frac{1.8 + 2.0 + 1.7 + 1.9 + 1.6}{5} = 1.8$$\n",
    "\n",
    "It is traditional to use the symbol $\\mu$ (mu) to denote the mean.\n",
    "\n",
    "We can formalize this computation with the equation\n",
    "\n",
    "$$ \\mu = \\frac{1}{n}\\sum^n_{i=1} x_i$$\n",
    "\n",
    "NumPy provides `numpy.mean()` for computing the mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [1.8, 2.0, 1.7, 1.9, 1.6]\n",
    "np.mean(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a convenience NumPy arrays provide the method `mean()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([1.8, 2.0, 1.7, 1.9, 1.6])\n",
    "x.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The *mode* of a set of numbers is the number that occurs most often. If only one number occurs most often we say it is a *unimodal* set, and if two or more numbers occur the most with equal frequency than the set is *multimodal*. For example the set {1, 2, 2, 2, 3, 4, 4, 4} has modes 2 and 4, which is multimodal, and the set {5, 7, 7, 13} has the mode 7, and so it is unimodal. We will not be computing the mode in this manner in this book, but we do use the concepts of unimodal and multimodal in a more general sense. For example, in the **Discrete Bayes** chapter we talked about our belief in the dog's position as a *multimodal distribution* because we assigned different probabilities to different positions.\n",
    "\n",
    "Finally, the *median* of a set of numbers is the middle point of the set so that half the values are below the median and half are above the median. Here, above and below is in relation to the set being sorted.  If the set contains an even number of values then the two middle numbers are averaged together.\n",
    "\n",
    "Numpy provides `numpy.median()` to compute the median. As you can see the median of {1.8, 2.0, 1.7, 1.9, 1.6} is 1.8, because 1.8 is the third element of this set after being sorted. In this case the median equals the mean, but that is not generally true."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Expected Value of a Random Variable\n",
    "\n",
    "The [*expected value*](https://en.wikipedia.org/wiki/Expected_value) of a random variable is the average value it would have if we took an infinite number of samples of it and then averaged those samples together. Let's say we have $x=[1,3,5]$ and each value is equally probable. What value would we *expect* $x$ to have, on average?\n",
    "\n",
    "It would be the average of 1, 3, and 5, of course, which is 3. That should make sense; we would expect equal numbers of 1, 3, and 5 to occur, so $(1+3+5)/3=3$ is clearly the average of that infinite series of samples. In other words, here the expected value is the *mean* of the sample space.\n",
    "\n",
    "Now suppose that each value has a different probability of happening. Say 1 has an 80% chance of occurring, 3 has an 15% chance, and 5 has only a 5% chance. In this case we compute the expected value by multiplying each value of $x$ by the percent chance of it occurring, and summing the result. For this case we could compute\n",
    "\n",
    "$$\\mathbb E[X] = (1)(0.8) + (3)(0.15) + (5)(0.05) = 1.5$$\n",
    "\n",
    "Here I have introduced the notation $\\mathbb E[X]$ for the expected value of $x$. Some texts use $E(x)$. The value 1.5 for $x$ makes intuitive sense because $x$ is far more likely to be 1 than 3 or 5, and 3 is more likely than 5 as well.\n",
    "\n",
    "We can formalize this by letting $x_i$ be the $i^{th}$ value of $X$, and $p_i$ be the probability of its occurrence. This gives us\n",
    "\n",
    "$$\\mathbb E[X] = \\sum_{i=1}^n p_ix_i$$\n",
    "\n",
    "A trivial bit of algebra shows that if the probabilities are all equal, the expected value is the same as the mean:\n",
    "\n",
    "$$\\mathbb E[X] = \\sum_{i=1}^n p_ix_i = \\frac{1}{n}\\sum_{i=1}^n x_i = \\mu_x$$\n",
    "\n",
    "If $x$ is continuous we substitute the sum for an integral, like so\n",
    "\n",
    "$$\\mathbb E[X] = \\int_{a}^b\\, xf(x) \\,dx$$\n",
    "\n",
    "where $f(x)$ is the probability distribution function of $x$. We won't be using this equation yet, but we will be using it in the next chapter.\n",
    "\n",
    "We can write a bit of Python to simulate this. Here I take 1,000,000 samples and compute the expected value of the distribution we just computed analytically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.500406"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total = 0\n",
    "N = 1000000\n",
    "for r in np.random.rand(N):\n",
    "    if r <= .80: total += 1\n",
    "    elif r < .95: total += 3\n",
    "    else: total += 5\n",
    "\n",
    "total / N"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see that the computed value is close to the analytically derived value. It is not exact because getting an exact values requires an infinite sample size."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "What is the expected value of a die role?\n",
    "\n",
    "### Solution\n",
    "\n",
    "Each side is equally likely, so each has a probability of 1/6. Hence\n",
    "$$\\begin{aligned}\n",
    "\\mathbb E[X] &= 1/6\\times1 + 1/6\\times 2 + 1/6\\times 3 + 1/6\\times 4 + 1/6\\times 5 + 1/6\\times6 \\\\\n",
    "&= 1/6(1+2+3+4+5+6)\\\\&= 3.5\\end{aligned}$$\n",
    "\n",
    "### Exercise\n",
    "\n",
    "Given the uniform continuous distribution\n",
    "\n",
    "$$f(x) = \\frac{1}{b - a}$$\n",
    "\n",
    "compute the expected value for $a=0$ and $B=20$.\n",
    "\n",
    "### Solution\n",
    "$$\\begin{aligned}\n",
    "\\mathbb E[X] &= \\int_0^{20}\\, x\\frac{1}{20} \\,dx \\\\\n",
    "&= \\bigg[\\frac{x^2}{40}\\bigg]_0^{20} \\\\\n",
    "&= 10 - 0 \\\\\n",
    "&= 10\n",
    "\\end{aligned}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variance of a Random Variable\n",
    "\n",
    "The computation above tells us the average height of the students, but it doesn't tell us everything we might want to know. For example, suppose we have three classes of students, which we label $X$, $Y$, and $Z$, with these heights:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = [1.8, 2.0, 1.7, 1.9, 1.6]\n",
    "Y = [2.2, 1.5, 2.3, 1.7, 1.3]\n",
    "Z = [1.8, 1.8, 1.8, 1.8, 1.8]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using NumPy we see that the mean height of each class is the same. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.8 1.8 1.8\n"
     ]
    }
   ],
   "source": [
    "print(np.mean(X), np.mean(Y), np.mean(Z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean of each class is 1.8 meters, but notice that there is a much greater amount of variation in the heights in the second class than in the first class, and that there is no variation at all in the third class.\n",
    "\n",
    "The mean tells us something about the data, but not the whole story. We want to be able to specify how much *variation* there is between the heights of the students. You can imagine a number of reasons for this. Perhaps a school district needs to order 5,000 desks, and they want to be sure they buy sizes that accommodate the range of heights of the students. \n",
    "\n",
    "Statistics has formalized this concept of measuring variation into the notion of [*standard deviation*](https://en.wikipedia.org/wiki/Standard_deviation) and [*variance*](https://en.wikipedia.org/wiki/Variance). The equation for computing the variance is\n",
    "\n",
    "$$\\mathit{VAR}(X) = \\mathbb  E[(X - \\mu)^2]$$\n",
    "\n",
    "Ignoring the square for a moment, you can see that the variance is the *expected value* for how much the sample space $X$ varies from the mean $\\mu:$ ($X-\\mu)$. I will explain the purpose of the squared term later. The formula for the expected value is $\\mathbb E[X] = \\sum\\limits_{i=1}^n p_ix_i$ so we can substitute that into the equation above to get\n",
    "\n",
    "$$\\mathit{VAR}(X) = \\frac{1}{n}\\sum_{i=1}^n (x_i - \\mu)^2$$\n",
    " \n",
    "Let's compute the variance of the three classes to see what values we get and to become familiar with this concept.\n",
    "\n",
    "The mean of $X$ is 1.8 ($\\mu_x = 1.8$) so we compute\n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\mathit{VAR}(X) &=\\frac{(1.8-1.8)^2 + (2-1.8)^2 + (1.7-1.8)^2 + (1.9-1.8)^2 + (1.6-1.8)^2} {5} \\\\\n",
    "&= \\frac{0 + 0.04 + 0.01 + 0.01 + 0.04}{5} \\\\\n",
    "\\mathit{VAR}(X)&= 0.02 \\, m^2\n",
    "\\end{aligned}$$\n",
    "\n",
    "NumPy provides the function `var()` to compute the variance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.02 meters squared\n"
     ]
    }
   ],
   "source": [
    "print(\"{:.2f} meters squared\".format(np.var(X)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is perhaps a bit hard to interpret. Heights are in meters, yet the variance is meters squared. Thus we have a more commonly used measure, the *standard deviation*, which is defined as the square root of the variance:\n",
    "\n",
    "$$\\sigma = \\sqrt{\\mathit{VAR}(X)}=\\sqrt{\\frac{1}{n}\\sum_{i=1}^n(x_i - \\mu)^2}$$\n",
    "\n",
    "It is typical to use $\\sigma$ for the *standard deviation* and $\\sigma^2$ for the *variance*. In most of this book I will be using $\\sigma^2$ instead of $\\mathit{VAR}(X)$ for the variance; they symbolize the same thing.\n",
    "\n",
    "For the first class we compute the standard deviation with\n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\sigma_x &=\\sqrt{\\frac{(1.8-1.8)^2 + (2-1.8)^2 + (1.7-1.8)^2 + (1.9-1.8)^2 + (1.6-1.8)^2} {5}} \\\\\n",
    "&= \\sqrt{\\frac{0 + 0.04 + 0.01 + 0.01 + 0.04}{5}} \\\\\n",
    "\\sigma_x&= 0.1414\n",
    "\\end{aligned}$$\n",
    "\n",
    "We can verify this computation with the NumPy method `numpy.std()` which computes the standard deviation. 'std' is a common abbreviation for standard deviation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "std 0.1414\n",
      "var 0.0200\n"
     ]
    }
   ],
   "source": [
    "print('std {:.4f}'.format(np.std(X)))\n",
    "print('var {:.4f}'.format(np.std(X)**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And, of course, $0.1414^2 = 0.02$, which agrees with our earlier computation of the variance.\n",
    "\n",
    "What does the standard deviation signify? It tells us how much the heights vary amongst themselves. \"How much\" is not a mathematical term. We will be able to define it much more precisely once we introduce the concept of a Gaussian in the next section. For now I'll say that for many things 68% of all values lie within one standard deviation of the mean. In other words we can conclude that for a random class 68% of the students will have heights between 1.66 (1.8-0.1414) meters and 1.94 (1.8+0.1414) meters. \n",
    "\n",
    "We can view this in a plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d9169a12b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from kf_book.gaussian_internal import plot_height_std\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plot_height_std(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For only 5 students we obviously will not get exactly 68% within one standard deviation. We do see that 3 out of 5 students are within $\\pm1\\sigma$, or 60%, which is as close as you can get to 68% with only 5 samples. Let's look at the results for a class with 100 students.\n",
    "\n",
    ">  We write one standard deviation as  $1\\sigma$, which is pronounced \"one standard deviation\", not \"one sigma\". Two standard deviations is $2\\sigma$, and so on."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d9173e5f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean = 1.789\n",
      "std  = 0.137\n"
     ]
    }
   ],
   "source": [
    "from numpy.random import randn\n",
    "data = 1.8 + randn(100)*.1414\n",
    "mean, std = data.mean(), data.std()\n",
    "\n",
    "plot_height_std(data, lw=2)\n",
    "print('mean = {:.3f}'.format(mean))\n",
    "print('std  = {:.3f}'.format(std))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By eye roughly 68% of the heights lie within $\\pm1\\sigma$ of the mean 1.8, but we can verify this with code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "71.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum((data > mean-std) & (data < mean+std)) / len(data) * 100."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll discuss this in greater depth soon. For now let's compute the standard deviation for \n",
    "\n",
    "$$Y = [2.2, 1.5, 2.3, 1.7, 1.3]$$\n",
    "\n",
    "The mean of $Y$ is $\\mu=1.8$ m, so \n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\sigma_y &=\\sqrt{\\frac{(2.2-1.8)^2 + (1.5-1.8)^2 + (2.3-1.8)^2 + (1.7-1.8)^2 + (1.3-1.8)^2} {5}} \\\\\n",
    "&= \\sqrt{0.152} = 0.39 \\ m\n",
    "\\end{aligned}$$\n",
    "\n",
    "We will verify that with NumPy with"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "std of Y is 0.39 m\n"
     ]
    }
   ],
   "source": [
    "print('std of Y is {:.2f} m'.format(np.std(Y)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This corresponds with what we would expect. There is more variation in the heights for $Y$, and the standard deviation is larger.\n",
    "\n",
    "Finally, let's compute the standard deviation for $Z$. There is no variation in the values, so we would expect the standard deviation to be zero.\n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\sigma_z &=\\sqrt{\\frac{(1.8-1.8)^2 + (1.8-1.8)^2 + (1.8-1.8)^2 + (1.8-1.8)^2 + (1.8-1.8)^2} {5}} \\\\\n",
    "&= \\sqrt{\\frac{0+0+0+0+0}{5}} \\\\\n",
    "\\sigma_z&= 0.0 \\ m\n",
    "\\end{aligned}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n"
     ]
    }
   ],
   "source": [
    "print(np.std(Z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we continue I need to point out that I'm ignoring that on average  men are taller than women. In general the height variance of a class that contains only men or women will be smaller than a class with both sexes. This is true for other factors as well. Well nourished children are taller than malnourished children. Scandinavians are taller than Italians. When designing experiments statisticians need to take these factors into account. \n",
    "\n",
    "I suggested we might be performing this analysis to order desks for a school district.  For each age group there are likely to be two different means - one clustered around the mean height of the females, and a second mean clustered around the mean heights of the males. The mean of the entire class will be somewhere between the two. If we bought desks for the mean of all students we are likely to end up with desks that fit neither the males or females in the school! \n",
    "\n",
    "We will not to consider these issues in this book.  Consult any standard probability text if you need to learn techniques to deal with these issues."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Why the Square of the Differences\n",
    "\n",
    "Why are we taking the *square* of the differences for the variance? I could go into a lot of math, but let's look at this in a simple way. Here is a chart of the values of $X$ plotted against the mean for $X=[3,-3,3,-3]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d91761b4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = [3, -3, 3, -3]\n",
    "mean = np.average(X)\n",
    "for i in range(len(X)):\n",
    "    plt.plot([i ,i], [mean, X[i]], color='k')\n",
    "plt.axhline(mean)\n",
    "plt.xlim(-1, len(X))\n",
    "plt.tick_params(axis='x', labelbottom=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we didn't take the square of the differences the signs would cancel everything out:\n",
    "\n",
    "$$\\frac{(3-0) + (-3-0) + (3-0) + (-3-0)}{4} = 0$$\n",
    "\n",
    "This is clearly incorrect, as there is more than 0 variance in the data. \n",
    "\n",
    "Maybe we can use the absolute value? We can see by inspection that the result is $12/4=3$ which is certainly correct — each value varies by 3 from the mean. But what if we have $Y=[6, -2, -3, 1]$? In this case we get $12/4=3$. $Y$ is clearly more spread out than $X$, but the computation yields the same variance. If we use the formula using squares we get a variance of 3.5 for $Y$, which reflects its larger variation.\n",
    "\n",
    "This is not a proof of correctness. Indeed, Carl Friedrich Gauss, the inventor of the technique, recognized that it is somewhat arbitrary. If there are outliers then squaring the difference gives disproportionate weight to that term. For example, let's see what happens if we have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance of X with outlier    = 621.45\n",
      "Variance of X without outlier =   2.03\n"
     ]
    }
   ],
   "source": [
    "X = [1, -1, 1, -2, -1, 2, 1, 2, -1, 1, -1, 2, 1, -2, 100]\n",
    "print('Variance of X with outlier    = {:6.2f}'.format(np.var(X)))\n",
    "print('Variance of X without outlier = {:6.2f}'.format(np.var(X[:-1])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Is this \"correct\"? You tell me. Without the outlier of 100 we get $\\sigma^2=2.03$, which accurately reflects how $X$ is varying absent the outlier. The one outlier swamps the variance computation. Do we want to swamp the computation so we know there is an outlier, or robustly incorporate the outlier and still provide an estimate close to the value absent the outlier? Again, you tell me. Obviously it depends on your problem.\n",
    "\n",
    "I will not continue down this path; if you are interested you might want to look at the work that James Berger has done on this problem, in a field called *Bayesian robustness*, or the excellent publications on *robust statistics* by Peter J. Huber [3]. In this book we will always use variance and standard deviation as defined by Gauss.\n",
    "\n",
    "The point to gather from this is that these *summary* statistics always tell an incomplete story about our data. In this example variance as defined by Gauss does not tell us we have a single large outlier. However, it is a powerful tool, as we can concisely describe a large data set with a few numbers. If we had 1 billion data points we would not want to inspect plots by eye or look at lists of numbers; summary statistics give us a way to describe the shape of the data in a useful way."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussians\n",
    "\n",
    "We are now ready to learn about [Gaussians](https://en.wikipedia.org/wiki/Gaussian_function). Let's remind ourselves of the motivation for this chapter.\n",
    "\n",
    "> We desire a unimodal, continuous way to represent probabilities that models how the real world works, and that is computationally efficient to calculate.\n",
    "\n",
    "Let's look at a graph of a Gaussian distribution to get a sense of what we are talking about."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d917603f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from filterpy.stats import plot_gaussian_pdf\n",
    "plot_gaussian_pdf(mean=1.8, variance=0.1414**2, \n",
    "                  xlabel='Student Height', ylabel='pdf');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This curve is a [*probability density function*](https://en.wikipedia.org/wiki/Probability_density_function) or *pdf* for short. It shows the relative likelihood  for the random variable to take on a value. We can tell from the chart student is somewhat more likely to have a height near 1.8 m than 1.7 m, and far more likely to have a height of 1.9 m vs 1.4 m. Put another way, many students will have a height near 1.8 m, and very few students will have a height of 1.4 m or 2.2 meters. Finally, notice that the curve is centered over the mean of 1.8 m.\n",
    "\n",
    "> I explain how to plot Gaussians, and much more, in the Notebook *Computing_and_Plotting_PDFs* in the \n",
    "Supporting_Notebooks folder. You can read it online [here](https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/Supporting_Notebooks/Computing_and_plotting_PDFs.ipynb) [1].\n",
    "\n",
    "This may be recognizable to you as a 'bell curve'. This curve is ubiquitous because under real world conditions many observations are distributed in such a manner. I will not use the term 'bell curve' to refer to a Gaussian because many probability distributions have a similar bell curve shape. Non-mathematical sources might not be as precise, so be judicious in what you conclude when you see the term used without definition.\n",
    "\n",
    "This curve is not unique to heights — a vast amount of natural phenomena exhibits this sort of distribution, including the sensors that we use in filtering problems. As we will see, it also has all the attributes that we are looking for — it represents a unimodal belief or value as a probability, it is continuous, and it is computationally efficient. We will soon discover that it also has other desirable qualities which we may not realize we desire.\n",
    "\n",
    "To further motivate you, recall the shapes of the probability distributions in the *Discrete Bayes* chapter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d91745b160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import kf_book.book_plots as book_plots\n",
    "belief = [0., 0., 0., 0.1, 0.15, 0.5, 0.2, .15, 0, 0]\n",
    "book_plots.bar_plot(belief)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "They were not perfect Gaussian curves, but they were similar. We will be using Gaussians to replace the discrete probabilities used in that chapter!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nomenclature\n",
    "\n",
    "A bit of nomenclature before we continue - this chart depicts the *probability density* of a *random variable* having any value between ($-\\infty..\\infty)$. What does that mean? Imagine we take an infinite number of infinitely precise measurements of the speed of automobiles on a section of highway. We could then plot the results by showing the relative number of cars going past at any given speed. If the average was 120 kph, it might look like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d917486630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_gaussian_pdf(mean=120, variance=17**2, xlabel='speed(kph)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The y-axis depicts the *probability density* — the relative amount of cars that are going the speed at the corresponding x-axis. I will explain this further in the next section.\n",
    "\n",
    "The Gaussian model is imperfect. Though these charts do not show it, the *tails* of the distribution extend out to infinity. *Tails* are the far ends of the curve where the values are the lowest. Of course human heights or automobile speeds cannot be less than zero, let alone $-\\infty$ or $\\infty$. “The map is not the territory” is a common expression, and it is true for Bayesian filtering and statistics. The Gaussian distribution above models the distribution of the measured automobile speeds, but being a model it is necessarily imperfect. The difference between model and reality will come up again and again in these filters. Gaussians are used in many branches of mathematics, not because they perfectly model reality, but because they are easier to use than any other relatively accurate choice. However, even in this book Gaussians will fail to model reality, forcing us to use computationally expensive alternatives. \n",
    "\n",
    "You will hear these distributions called *Gaussian distributions* or *normal distributions*.  *Gaussian* and *normal* both mean the same thing in this context, and are used interchangeably. I will use both throughout this book as different sources will use either term, and I want you to be used to seeing both. Finally, as in this paragraph, it is typical to shorten the name and talk about a *Gaussian* or *normal* — these are both typical shortcut names for the *Gaussian distribution*. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussian Distributions\n",
    "\n",
    "Let's explore how Gaussians work. A Gaussian is a *continuous probability distribution* that is completely described with two parameters, the mean ($\\mu$) and the variance ($\\sigma^2$). It is defined as:\n",
    "\n",
    "$$ \n",
    "f(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} \\exp\\big [{-\\frac{(x-\\mu)^2}{2\\sigma^2} }\\big ]\n",
    "$$\n",
    "\n",
    "$\\exp[x]$ is notation for $e^x$.\n",
    "\n",
    "<p> Don't be dissuaded by the equation if you haven't seen it before; you will not need to memorize or manipulate it. The computation of this function is stored in `stats.py` with the function `gaussian(x, mean, var, normed=True)`. \n",
    "    \n",
    "Shorn of the constants, you can see it is a simple exponential:\n",
    "    \n",
    "$$f(x)\\propto e^{-x^2}$$\n",
    "\n",
    "which has the familiar bell curve shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d917414908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-3, 3, .01)\n",
    "plt.plot(x, np.exp(-x**2));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's remind ourselves how to look at the code for a function. In a cell, type the function name followed by two question marks and press CTRL+ENTER. This will open a popup window displaying the source. Uncomment the next cell and try it now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from filterpy.stats import gaussian\n",
    "#gaussian??"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot a Gaussian with a mean of 22 $(\\mu=22)$, with a variance of 4 $(\\sigma^2=4)$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d91756c5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_gaussian_pdf(22, 4, mean_line=True, xlabel='$^{\\circ}C$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What does this curve *mean*? Assume we have a thermometer which reads 22°C. No thermometer is perfectly accurate, and so we expect that each reading will be slightly off the actual value. However, a theorem called  [*Central Limit Theorem*](https://en.wikipedia.org/wiki/Central_limit_theorem) states that if we make many measurements that the measurements will be normally distributed. When we look at this chart we can see it is proportional to the probability of the thermometer reading a particular value given the actual temperature of 22°C. \n",
    "\n",
    "Recall that a Gaussian distribution is *continuous*. Think of an infinitely long straight line - what is the probability that a point you pick randomly is at 2. Clearly 0%, as there is an infinite number of choices to choose from. The same is true for normal distributions; in the graph above the probability of being *exactly* 2°C is 0% because there are an infinite number of values the reading can take.\n",
    "\n",
    "What is this curve? It is something we call the *probability density function.* The area under the curve at any region gives you the probability of those values. So, for example, if you compute the area under the curve between 20 and 22 the resulting area will be the probability of the temperature reading being between those two temperatures. \n",
    "\n",
    "Here is another way to understand it. What is the *density* of a rock, or a sponge? It is a measure of how much mass is compacted into a given space. Rocks are dense, sponges less so. So, if you wanted to know how much a rock weighed but didn't have a scale, you could take its volume and multiply by its density. This would give you its mass. In practice density varies in most objects, so you would integrate the local density across the rock's volume.\n",
    "\n",
    "$$M = \\iiint_R p(x,y,z)\\, dV$$\n",
    "\n",
    "We do the same with *probability density*. If you want to know the temperature being between 20°C and 21°C kph you would integrate the curve above from 20 to 21. As you know the integral of a curve gives you the area under the curve. Since this is a curve of the probability density, the integral of the density is the probability. \n",
    "\n",
    "What is the probability of a the temperature being exactly 22°C? Intuitively, 0. These are real numbers, and the odds of 22°C vs, say, 22.00000000000017°C is infinitesimal. Mathematically, what would we get if we integrate from 22 to 22? Zero. \n",
    "\n",
    "Thinking back to the rock, what is the weight of an single point on the rock? An infinitesimal point must have no weight. It makes no sense to ask the weight of a single point, and it makes no sense to ask about the probability of a continuous distribution having a single value. The answer for both is obviously zero.\n",
    "\n",
    "In practice our sensors do not have infinite precision, so a reading of 22°C implies a range, such as 22 $\\pm$ 0.1°C, and we can compute the probability of that range by integrating from 21.9 to 22.1.\n",
    "\n",
    "We can think of this in Bayesian terms or frequentist terms. As a Bayesian, if the thermometer reads exactly 22°C, then our belief is described by the curve - our belief that the actual (system) temperature is near 22°C is very high, and our belief that the actual temperature is near 18 is very low. As a frequentist we would say that if we took 1 billion temperature measurements of a system at exactly 22°C, then a histogram of the measurements would look like this curve. \n",
    "\n",
    "How do you compute the probability, or area under the curve? You integrate the equation for the Gaussian \n",
    "\n",
    "$$ \\int^{x_1}_{x_0}  \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{1}{2}{(x-\\mu)^2}/\\sigma^2 } dx$$\n",
    "\n",
    "This is called the *cumulative probability distribution*, commonly abbreviated *cdf*.\n",
    "\n",
    "I wrote `filterpy.stats.norm_cdf` which computes the integral for you. For example, we can compute"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cumulative probability of range 21.5 to 22.5 is 19.74%\n",
      "Cumulative probability of range 23.5 to 24.5 is 12.10%\n"
     ]
    }
   ],
   "source": [
    "from filterpy.stats import norm_cdf\n",
    "print('Cumulative probability of range 21.5 to 22.5 is {:.2f}%'.format(\n",
    "      norm_cdf((21.5, 22.5), 22,4)*100))\n",
    "print('Cumulative probability of range 23.5 to 24.5 is {:.2f}%'.format(\n",
    "      norm_cdf((23.5, 24.5), 22,4)*100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean ($\\mu$) is what it sounds like — the average of all possible probabilities. Because of the symmetric shape of the curve it is also the tallest part of the curve. The thermometer reads 22°C, so that is what we used for the mean.  \n",
    "\n",
    "The notation for a normal distribution for a random variable $X$ is $X \\sim\\ \\mathcal{N}(\\mu,\\sigma^2)$ where $\\sim$ means *distributed according to*. This means I can express the temperature reading of our thermometer as\n",
    "\n",
    "$$\\text{temp} \\sim \\mathcal{N}(22,4)$$\n",
    "\n",
    "This is an extremely important result. Gaussians allow me to capture an infinite number of possible values with only two numbers! With the values $\\mu=22$ and $\\sigma^2=4$ I can compute the distribution of measurements for over any range.\n",
    "\n",
    "Some sources use $\\mathcal N (\\mu, \\sigma)$ instead of $\\mathcal N (\\mu, \\sigma^2)$. Either is fine, they are both conventions. You need to keep in mind which form is being used if you see a term such as $\\mathcal{N}(22,4)$. In this book I always use $\\mathcal N (\\mu, \\sigma^2)$, so $\\sigma=2$, $\\sigma^2=4$ for this example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Variance and Belief\n",
    "\n",
    "Since this is a probability density distribution it is required that the area under the curve always equals one. This should be intuitively clear — the area under the curve represents all possible outcomes, *something* happened, and the probability of *something happening* is one, so the density must sum to one. We can prove this ourselves with a bit of code. (If you are mathematically inclined, integrate the Gaussian equation from $-\\infty$ to $\\infty$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "print(norm_cdf((-1e8, 1e8), mu=0, var=4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This leads to an important insight. If the variance is small the curve will be narrow. this is because the variance is a measure of *how much* the samples vary from the mean. To keep the area equal to 1, the curve must also be tall. On the other hand if the variance is large the curve will be wide, and thus it will also have to be short to make the area equal to 1.\n",
    "\n",
    "Let's look at that graphically. We will use the aforementioned `filterpy.stats.gaussian` which can take either a single value or array of values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.24197072451914337\n",
      "[0.378 0.622]\n"
     ]
    }
   ],
   "source": [
    "from filterpy.stats import gaussian\n",
    "\n",
    "print(gaussian(x=3.0, mean=2.0, var=1))\n",
    "print(gaussian(x=[3.0, 2.0], mean=2.0, var=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default `gaussian` normalizes the output, which turns the output back into a probability distribution. Use the argument`normed` to control this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.242 0.399]\n"
     ]
    }
   ],
   "source": [
    "print(gaussian(x=[3.0, 2.0], mean=2.0, var=1, normed=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the Gaussian is not normalized it is called a *Gaussian function* instead of *Gaussian distribution*.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d917a45160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.arange(15, 30, 0.05)\n",
    "plt.plot(xs, gaussian(xs, 23, 0.2**2), label='$\\sigma^2=0.2^2$')\n",
    "plt.plot(xs, gaussian(xs, 23, .5**2), label='$\\sigma^2=0.5^2$', ls=':')\n",
    "plt.plot(xs, gaussian(xs, 23, 1**2), label='$\\sigma^2=1^2$', ls='--')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is this telling us? The Gaussian with $\\sigma^2=0.2^2$ is very narrow. It is saying that we believe $x=23$, and that we are very sure about that: within $\\pm 0.2$ std. In contrast, the Gaussian with $\\sigma^2=1^2$ also believes that $x=23$, but we are much less sure about that. Our belief that $x=23$ is lower, and so our belief about the likely possible values for $x$ is spread out — we think it is quite likely that $x=20$ or $x=26$, for example. $\\sigma^2=0.2^2$ has almost completely eliminated $22$ or $24$ as possible values, whereas $\\sigma^2=1^2$ considers them nearly as likely as $23$.\n",
    "\n",
    "If we think back to the thermometer, we can consider these three curves as representing the readings from three different thermometers. The curve for $\\sigma^2=0.2^2$ represents a very accurate thermometer, and curve for $\\sigma^2=1^2$ represents a fairly inaccurate one. Note the very powerful property the Gaussian distribution affords us — we can entirely represent both the reading and the error of a thermometer with only two numbers — the mean and the variance.\n",
    "\n",
    "An equivalent formation for a Gaussian is $\\mathcal{N}(\\mu,1/\\tau)$ where $\\mu$ is the *mean* and $\\tau$ the *precision*. $1/\\tau = \\sigma^2$; it is the reciprocal of the variance. While we do not use this formulation in this book, it underscores that the variance is a measure of how precise our data is. A small variance yields large precision — our measurement is very precise. Conversely, a large variance yields low precision — our belief is spread out across a large area. You should become comfortable with thinking about Gaussians in these equivalent forms. In Bayesian terms Gaussians reflect our *belief* about a measurement, they express the *precision* of the measurement, and they express how much *variance* there is in the measurements. These are all different ways of stating the same fact.\n",
    "\n",
    "I'm getting ahead of myself, but in the next chapters we will use Gaussians to express our belief in things like the estimated position of the object we are tracking, or the accuracy of the sensors we are using."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The  68-95-99.7 Rule\n",
    "\n",
    "It is worth spending a few words on standard deviation now. The standard deviation is a measure of how much the data deviates from the mean. For Gaussian distributions, 68% of all the data falls within one standard deviation ($\\pm1\\sigma$) of the mean, 95% falls within two standard deviations ($\\pm2\\sigma$), and 99.7% within three ($\\pm3\\sigma$). This is often called the [68-95-99.7 rule](https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule). If you were told that the average test score in a class was 71 with a standard deviation of 9.4, you could conclude that 95% of the students received a score between 52.2 and 89.8 if the distribution is normal (that is calculated with $71 \\pm (2 * 9.4)$). \n",
    "\n",
    "Finally, these are not arbitrary numbers. If the Gaussian for our position is $\\mu=22$ meters, then the standard deviation also has units meters. Thus $\\sigma=0.2$ implies that 68% of the measurements range from 21.8 to 22.2 meters. Variance is the standard deviation squared, thus $\\sigma^2 = .04$ meters$^2$. As you saw in the last section, writing $\\sigma^2 = 0.2^2$ can make this somewhat more meaningful, since the 0.2 is in the same units as the data.\n",
    "\n",
    "The following graph depicts the relationship between the standard deviation and the normal distribution. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d9179be128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from kf_book.gaussian_internal import display_stddev_plot\n",
    "display_stddev_plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interactive Gaussians\n",
    "\n",
    "For those that are reading this in a Jupyter Notebook, here is an interactive version of the Gaussian plots. Use the sliders to modify $\\mu$ and $\\sigma^2$. Adjusting $\\mu$ will move the graph to the left and right because you are adjusting the mean, and adjusting $\\sigma^2$ will make the bell curve thicker and thinner."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "592797026a1346119330de5fe1ef9016",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(FloatSlider(value=5.0, description='mu', max=7.0, min=3.0), FloatSlider(value=0.03, description='variance', max=1.0, min=0.01), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "from ipywidgets import interact, FloatSlider\n",
    "\n",
    "def plt_g(mu,variance):\n",
    "    plt.figure()\n",
    "    xs = np.arange(2, 8, 0.01)\n",
    "    ys = gaussian(xs, mu, variance)\n",
    "    plt.plot(xs, ys)\n",
    "    plt.ylim(0, 0.04)\n",
    "\n",
    "interact(plt_g, mu=FloatSlider(value=5, min=3, max=7),\n",
    "         variance=FloatSlider(value = .03, min=.01, max=1.));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, if you are reading this online, here is an animation of a Gaussian. First, the mean is shifted to the right. Then the mean is centered at $\\mu=5$ and the variance is modified.\n",
    "\n",
    "<img src='animations/04_gaussian_animate.gif'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computational Properties of Gaussians\n",
    "\n",
    "The discrete Bayes filter works by multiplying and adding arbitrary probability distributions. The Kalman filter uses Gaussians instead of arbitrary distributions, but the rest of the algorithm remains the same. This means we will need to multiply and add Gaussians. \n",
    "\n",
    "A remarkable property of Gaussian distributions is that the sum of two independent Gaussians is another Gaussian! The product is not Gaussian, but proportional to a Gaussian. There we can say that the result of multipying two Gaussian distributions is a Gaussian function (recall function in this context means that the property that the values sum to one is not guaranteed).\n",
    "\n",
    "Before we do the math, let's test this visually. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6JGflScZfOlZ5jPvev49An0D2LNvDSL+RTqm3v4w7DZ1s/HQjS8cv5YaYG+QerGsg+7HyJGN1SM7Kc3XGjo4dZHCF6wdXQgghrs252nOUXC3h60lfd3VThBBCDEEyuOqHDK6EEEI4k8lkkrNXQggxRMlDhIUQQgx59W31rm4CzZ3NPHvyWVa9uwqjyejq5gghhHADMlugG6irq8NoNOLl5UVoaKirmzMkScbqkJyVJxlDVk0Wd++5mzvG38GPZ/7Y6WeNBpqxBg07c3ZyteMqH5d+zE2jb3JqO4Yy2Y+VJxmrQ3JWnqdlLIMrN1BcXGydYtITdhpPJBmrQ3JWnmQML59/mU5jJ02dTYpcjjfQjAN8Avj2+G/zUvZL/PPcP2Vw5QDZj5UnGatDclaep2UslwUKIYTwGDWtNewt3AvAdyZ+x8WtgVUTV6HVaDlaeZScKzmubo4QQggXc3hw1dTUxCOPPEJsbCx+fn5kZGSwa9euAZWtqqri3nvvJTw8nICAAGbNmsWBAwd6vO+dd97h7rvvZsqUKfj4+Az4l8n9+/ej0WjQaDTU1NQ4tF2uFBcXR0JCAnFxca5uypAlGatDclbecM/41QuvojfqSY9IJy08TZF1OJJx9IhoFiUuAmBnzk5F2jMUDff9WA2SsTokZ+V5WsYOXxa4bNkyjh07xqZNm5gwYQI7duxg5cqVGI1GVq1a1Wu59vZ2FixYQH19Pc888wyRkZFs3ryZJUuWsH//fubNm2d97+7duzly5AjTpk1Dp9Nx4sSJftvV1NTEd7/7XWJjYykvL3d0s1wqPDzc1U0Y8iRjdUjOyhvOGXcaO/lX7r8AZc9aOZrxytSV7C3cy56CPfxg+g8I9g1WqGVDx3Dej9UiGatDclaep2Xs0Jmr9957j3379rFlyxYeeOAB5s+fzwsvvMCiRYt49NFHbR7y1d3f//53srKy+Ne//sV3vvMdFi1axGuvvcaECRN47LHHbN77wgsvcOHCBV555RVuuOGGAbXtRz/6EaGhodx3332ObJIQQggP8VHJR9S01hDmF8bCxIWubo7VtMhpjBs5jlZ9K+/kv+Pq5gghhHAhhwZXu3fvJjAwkOXLl9u8vmbNGsrLy8nMzOyzbEpKCrNmzbK+5u3tzerVqzl69ChlZWVfNsrBZ0598sknPP/887z44ovydGwhhBiiXrvwGgBLxy/Fx8vHxa35kkaj4c6UOwHzZYvD7PGRQgghunBoFJOVlcXEiRPx9ra9mnDq1KnW5X2VtbzPXtns7GxHmmLV2trK2rVreeSRR7juuuuuqQ4hhBDuraypjM/KPwNg2bhlLm5NT7eOvRV/b38u1l/kZNVJVzdHCCGEizh0z1VtbS1jx47t8fqoUaOsy/sqa3mfo2X78tOf/hSDwcDPf/7zayoP5oFdYmIiwcFfXiff3t5OTo555qfQ0FASEhJsyuTl5dHS0gJAenq6zbKamhrrmbiEhASbaSMNBoN1EBoUFMTYsWM5ffq0dYrJ4OBgGhsbAZg8ebLNQLa+vp6ioiIAYmNjiYiIsFnvmTNnMJlM+Pv7M2HCBJtlJSUlXLlyBYCUlBT8/Pysy5qamsjPzwcgMjKSmJgYm7Lnzp2ztm/SpEk2yyoqKqiqqgIgOTmZwMBA67K2tjZyc3MB8+c8evRom7IXLlygtbUVjUbTY+BdXV1tvXcuMTGRkSNHWpfp9XrrYDw4OJgxY8bYlL106ZL1SdppaWlotVprxlqt1npmNC4ursd1vKdPnwYgICCA8ePH2ywrLi6mrq4OgNTUVHQ6nXVZY2MjBQUFAERFRREdHW1TNjs7G71ej06nIzU11WZZeXk51dXVAIwbN44RI0ZYl7W0tJCXlwdAWFgY8fHxNmVzc3Npa2tDq9WSlmZ7c39VVRUVFRUAJCUlERISYl3W0dHB+fPnAQgJCSEpKcmmbH5+Pk1NTQBMmTLF5mxybW0tpaWlAMTHxxMWFmZddurUKfR6PWD+3iQnJ9vUW1hYSENDAwATJ07E19fXuqyhoYHCwkIAYmJiiIyMtCmblZWFwWDAz8+PlJQUm2WlpaXWPmT8+PEEBARYlzU3N3Px4kUAIiIiiI2NtSmbk5NDe3s73t7eTJ482WZZZWUlly9fBmDMmDEu6yO6OnHihPXMSEZGxrDpIz4yfIQJEzfE3MDo4NFO7yMs6urqrNuq1WqZNm2aTdne+ogg3yBuDL+RfZX7eOnoS0xePFn6CHr2EUajkbNnz9LZ2QmAj4+PzfdD+gizwfQRBQUFNDY22s14KPcRSh9HWNTV1VFcXAyYjyPKysqs25aeni7HEV8YbB8BEBgYSHJyss1xckhIiOp9hOV7OlAOT2jR18x9/c3qN5iy9hw9epSnn36avXv34u/v73B5C71e3+MyDpPJZO2YLAeL3ctYlndnNBqty4xGY4/lA623e5u61mvv/rbOzk5MJhM+Pj0vlzEYDIOqt7dt7Vpv923tmqG9ei3bau+zH2i9jn42lu2xV2/XZY5+Nv1ta2dnJ3q93u4lr319NgOpt7Oz0+6yvuq1lO2vXnv627+7199bm7rrb1s7OjowGo12L/11Rob2MhpovWr2Ed3b0Fu9Q6mPMGHirYK3ALhjwh0O1Xstn03Xerrrq96bIm5iX+U+Muszae1stTlwkj6iZ732SB9h5qzjiL7qHUp9hJrHEUod40kf0bNedzqOcIRDg6uwsDC7Z5gsv2TYOzPljLK9ue+++1i2bBnTp0+nvr4eMP/KAeZfAHQ6HUFBQf3W4+3t3eOLqdForJ1L98sgLa/Z63zAfM+YZZm9L0H3egMCAtDr9Xh7e9vU271NXeu1t2P4+PhgMpnstler1Q6q3q7/7a3e7tvaNUN79Vq21V6nONB6B/rZWDLu+sUbyGfTW7197S+9Zdj1Pb1t67XUazAY7C7rq15L2b7qvZb9OyAgwPprX3/b2l1/2+rr64vBYFAkQ6PR6PD3Rs0+onu9lj/aw6WPON90nsstlwnyCWL+6PkO1Xstn41l+7sOjrpvq716p4ZNJdwnnJrOGj6p+ITbxt824G0dLn2EpazlILHrr8Pd29Sd9BG2beqvXr1ej7+/v806hmofocZxhEX3z6brMVzXbZTjiMH1EV3/2zVjV/URjtCYHBiOrVu3jp07d1JXV2ez0+zatYuVK1dy6NAhZs+ebbfs4sWLKSkpsZ5CtNi0aROPP/44ZWVlPU7FAzz00ENs3rzZ7qixv41NT0/n1KlTNq8ZjUbrwZ9FUFCQw5NoCCGEUMeTnz3JG3lvcMf4O/jZ7J+5ujl9evbks3xQ/AEPZTzEgsQFrm6OEEKIQXJ07ODQmaulS5fywgsv8Prrr3PXXXdZX9+2bRuxsbHMnDmzz7IPPvggmZmZ1vfp9Xq2b9/OzJkz7Q6s+nPw4MEer23dupVt27bx5ptveszDxoQQQvRubtxcqlqquC35tv7f7GLfS/8eD2U8dE2XugshhPB8Dg2ubr75ZhYtWsT69etpbGxk3Lhx7Ny5k71797J9+3brKbi1a9eybds28vPzSUxMBMyX8G3evJnly5ezadMmIiMj2bJlC7m5uezfv99mPUVFRRw7dgzAeoPka6+Zp+BNSkpi+vTpANx000092vjhhx8CMGfOHI976JgQQoieFiYudKvnWvXFnaaIF0IIoT6HJ7R444032LhxI0888QRXrlwhNTWVnTt3smLFCut7DAYDBoPB5lI+nU7HgQMHeOyxx3j44YdpaWkhIyODPXv2MG/ePJt1HDx4kDVr1ti8Znm21j333MPWrVsdbbYQQgihmpbOFg5XHGZBglwaKIQQw4lD91wNBe54z1VxcbH1Rr3uU7UK55CM1SE5K284ZVzfVs/rea9zy9hbiB4R3X8BJxlsxu2Gdha8uoCG9gZeu+01Ukal9F9omBlO+7GrSMbqkJyV5+qMHR07yCwObqCuro4rV65Yn30gnE8yVofkrLzhlPH7he/z9OdP818f/Jeq6x1sxjqtjhlRM0gISuBK2xUnt25oGE77satIxuqQnJXnaRk7fFmgEEIIoYboEdFMj5punX7dk/xizi8I9AmUiS2EEGKYkcsCcf1lge3t7ZhMJjQajd3nqojBk4zVITkrbzhmbNletQzHjNUmGStPMlaH5Kw8V2fs6NhBBle4fnAlhBBiaOowdFBytYTkkcmubooQQohrIPdcCSGE8Hh7C/dS01rj6mYMyrnac8x7ZR4P7HsAo8no6uYIIYRQgQyuhBBCuJWypjIe/ehRFr26iMaORlc355olj0zGaDJyueUyZ2vOuro5QgghVCATWriBxsZG67WkwcHBrm7OkCQZq0NyVt5wyPhA0QEAMiIzCPZVfxudlbFOq2Pe6HnsKdjDvsJ9pEekO7GVnm047MeuJhmrQ3JWnqdlLGeu3EBBQQF5eXkUFBS4uilDlmSsDslZecMh4/3F+wFYmLjQJet3ZsaLExcDsK9oH8PsFuc+DYf92NUkY3VIzsrztIxlcCWEEMJtVLdUc6rqFAALE1wzuHKmOXFz8Pf2p7y5nHO151zdHCGEEAqTywLdQFRUFAaDAa1W6+qmDFmSsTokZ+UN9YwPFB/AhImpEVOJGhHlkjY4M2N/b3/mxs3lP0X/4f2i95kcPtkJLfR8Q30/dgeSsTokZ+V5WsYyuHID0dHRrm7CkCcZq0NyVt5Qz3h/kfmSwEUJi1zWBmdnvDhpMf8p+g/7Cvfx/eu+Lw8WZujvx+5AMlaH5Kw8T8tYLgsUQgjhFura6jh++TgACxIXuLg1zjM3bi5+Wj9Km0rJuZLj6uYIIYRQkAyuhBBCuIWDJQcxmAykjkpldNBoVzfHaQJ8Argx7kbgy8k6hBBCDE0yuBJCCOEW9hXtA4bGRBbdzU+YD8BHJR+5uCVCCCGUJPdcuYHs7Gw6Ozvx8fFh8mS52VkJkrE6JGflDdWMmzubyazIBFw3BbuFEhnPjZuLl8aL3LpcypvKiQ2MdUq9nmqo7sfuRDJWh+SsPE/LWM5cuQG9Xm/9J5QhGatDclbeUM34cPlhOo2dJAQlMDZkrEvbokTGoX6hZERkAPBRqZy9Gqr7sTuRjNUhOSvP0zKWM1duQKfT4eXlhY+Pj6ubMmRJxuqQnJU3VDP+sORDAOaNnufy2fSUynhBwgK8NF5E+kc6tV5PNFT3Y3ciGatDclaep2WsMQ2zR8YbjUauXr1q81pQUBBeXnISTwgh1NauN9DQ0snHpR9zpOoDVqbeyfXR17m6WUIIIQTg+NhBBlfI4EoIIdTSrjfwyYUa9mZXcrK4jks1zXT9K+Tvo2VSbDA3jB3FLVNimRgT5PIzWUIIIYYvGVz1QwZXQgihvoaWTrYdLmTrZ4Vcae6wWabRgM7bi7ZOY49y6fEhrL8pmcWTovHyGhqDrNrWWgobC7k+6npXN0UIIUQ/ZHDVDxlcCSGEeoxGE/86XsJv9+ZQ19IJQFSwjm9MiWHu+HDS4kL4oPRN0iPTGRs8gZK6Vk6V1LPvXCUHc6vp0JsHXNcljOQXt6eRFhfiys0ZtOyabFa+u5KRupEcvPMgWi+tq5skhBCiDzK46oc7Dq7Ky8sxGAxotVpiY4f39LxKkYzVITkrz5MyvtzYxvdfOcVn+bUAjI8M5KGvjeOWKTF4a819bkVTBYtfX4yXxosP7/yQUL9Qa/mapna2HirkpUMFNHcY8NLAIwsnsGH+OLQKnsVSMuNOYyc3vXITcYFxPPu1Z4kaEeXU+j2FJ+3HnkoyVofkrDxXZ+zo2EFmC3QD1dXV1vn75YupDMlYHZKz8jwl48P5tWzY8TlXmjvw99Hyw6+ncPesRHy0tn+MWvWtzB89n3ZDu83ACiA8UMcPv57C6hsS+eW753j3TAV/3HeBw/m1bPnOdYSO8FWk7Upm7OPlw9479hLkG+TUej2Np+zHnkwyVofkrDxPy1gGV0IIIZzq1eMlPP7GWfRGE5Njg/nzymkkRwTafe/YkWP589f+TF8XUUSH+LF51XUsSC3lJ29mcfhSLcue+4z/vXcGY8JHKLUZihnuAyshhBjK5LJAXH9ZYHNzMyaTCY1Gw4gRnneg4AkkY3VIzspz94xf/OQSv3r3PAC3To3h98sIdZhKAAAgAElEQVTT8fNx3n1FFy5fZc1LxyirbyU80Jcd372BCVHOHayolXFLZwsAAT4Biq3DXbn7fjwUSMbqkJyV5+qMHR07ODyiaGpq4pFHHiE2NhY/Pz8yMjLYtWvXgMpWVVVx7733Eh4eTkBAALNmzeLAgQM93vfOO+9w9913M2XKFHx8fHqdhvfEiRNs2LCBKVOmEBQURFRUFAsXLuSDDz5wdLNcasSIEQQGBsqXUkGSsTokZ+W5c8YvfPzlwOqBeWP584ppfQ6sShpLKLla4tA6JkQFsXvDbCbFBFPT1MGK54+QU9k4qHZ3p0bGvz/2e27cdSPvXHpHsXW4M3fej4cKyVgdkrPyPC1jhwdXy5YtY9u2bTz55JPs2bOHGTNmsHLlSnbs2NFnufb2dhYsWMCBAwd45plneOutt4iKimLJkiV89NFHNu/dvXs3R44cYdKkSaSnp/da586dOzl69Cj33Xcfb731Fi+++CI6nY4FCxbwj3/8w9FNE0IIcY12HS3m1++ZB1b/tWA8P1qS2u/U6S9lv8Q33vgGz51+zqF1RQb5seO7M5kSF8KV5g7+z9+PUnKl5Zrb7gohuhA6jZ18UvaJq5sihBDCiRy6LPC9997jlltuYceOHaxcudL6+uLFi8nOzqa4uBit1v6vlFu2bGHDhg189tlnzJo1CwC9Xk96ejqBgYFkZmZa32s0Gq2n2h566CE2b95s93r8qqoqIiMjbV4zGAxcd911NDc3c/HixR5l3PGyQCGE8GT7z11m3T+PYzTB+puS+b9LUvstYzKZWPL6Esqby9myYAtz4+c6vN6G1k7u+tthciqvMiZ8BK99bxZhgbpr2QTVna89z53v3Im/tz+frvgUX60yk3MIIYQYHEUvC9y9ezeBgYEsX77c5vU1a9ZQXl5uM0CyVzYlJcU6sALw9vZm9erVHD16lLKysi8bNcCBTveBFYBWq+X666+npMSxS01cqaWlhebmZlpaPOuXV08iGatDclaeu2V8vqKR/9p1EqMJll8fz2NfTxlQuYLGAsqby/H18mV69PRrWneIvw/b7vsKcSP9KahpZv3Ln1ufizUYamScMiqFML8wWvWtnKw6qdh63JW77cdDkWSsDslZeZ6WsUODq6ysLCZOnIi3t+0kg1OnTrUu76us5X32ymZnZzvSlF7p9Xo++eQTJk+e7JT61JCXl8f58+fJy8tzdVOGLMlYHZKz8twp4yvNHXz3H8dp6TAwZ1wYTy2b0us9st0dKjsEwPTo6fh7+19zG6KC/dh23wwCdd4cLbjCz98e/N8SNTL20ngxJ24OAJ+WfarYetyVO+3HQ5VkrA7JWXmelrFDU7HX1tYyduzYHq+PGjXKuryvspb3OVrWET/72c+4ePEib7755oDLZGdnk5iYSHBwsPW19vZ2cnJyAAgNDSUhIcGmTF5ennUE3f2+sJqaGuuZuISEBEJDv3x2i8FgsA5Cg4KCeuRZUFBAY6P55uzJkyfbDGTr6+spKioCIDY2loiICJuyZ86cwWQy4e/vz4QJE2yWlZSUcOXKFQBSUlLw8/OzLmtqaiI/Px8wnw2MiYmxKXvu3Dnr8wUmTZpks6yiooKqqioAkpOTCQz8crrltrY2cnNzAfPnPHr0aJuyFy5coLW1FY1G02PgXV1dTXl5OQCJiYmMHDnSukyv11sH48HBwYwZM8am7KVLl6ynb9PS0mwuVTUajZw+fRqAuLg4wsPDbcpalgUEBDB+/HibZcXFxdTV1QGQmpqKTvfl5UeNjY0UFBQAEBUVRXR0tE3Z7Oxs9Ho9Op2O1FTbS6bKy8uprq4GYNy4cTY3bLa0tFg7k7CwMOLj423K5ubm0tbWhlarJS0tzWZZVVUVFRUVACQlJRESEmJd1tHRwfnz5vtjQkJCSEpKsimbn59PU1MTAFOmTLE5m1xbW0tpaSkA8fHxhIWFWZdZLt/t7OwkPz+f5ORkm3oLCwtpaGgAYOLEifj6fnkpVENDA4WFhQDExMT0ODOdlZWFwWDAz8+PlBTbsyOlpaXWPmT8+PEEBHw5+1rXS4QjIiJ6PCMjJyeH9vZ2vL29e/woU1lZyeXLlwEYM2aMW/QRer0eMGes1+td1kcYjSb+e9dJSutaiQ705ntTfcnLzRlwH2EZXCWRxOnTpwfdRzyzIoP7/3GclzOLSY8LJkVXDzjeR9TV1dHZ2QmY+4vunNlHzI2by7/z/82nZZ+yxH/JsOgjjEYjZ8+etWbcnfQRZs44jrCXsRxHmA3mOKKuro7i4mLAfBzRnRxHmA22jwAIDAx0i+MIR8+YOfycq75+lezvF8vBlB2IF198kV//+tf84Ac/4Pbbbx9wOb1e3+OeLpPJZO2YLAcz3cv09sfBaDT2+ce5e71hYWHWJ0+3trZal3dvU9d6DQaD3XpNJhM+Pj49lhkMhkHV29u2dq23+7Z2zdBevZYM7X32A613oJ+NJeOOjg7rl3Ign01v9fa1v/SWoV6vt3vJa1+fzUDq7ezstLusr3otZfur156+9u+wsDDrgYa98l3b1F1/29rR0YHRaLR7X6czMrSX0UDrVbqP6MrX15f29na7bVKzj3juo3w+yavBz8eLx+eG4e9l7Pczt2xrm76N45ePAzDJf1Kv+7AjfcSCiVF8f+EE/rjvAk++fY6n5ocyOtj7mj4bi65/XC2c2UfMip2Fl8aLi/UXqWyuJMQrZMj3EV3r9fHxsTmo6t6m7qSPsG3TQOoNCwuz+b7LcUTPegf72XQ9hrNs60DqleOI/vfvrvuxJeP29naX9BGOcGhwFRYWZvcMk+WXDHtnppxRdiBeeuklHnjgAdatW8fvfvc7h8p6e3v3+GJqNBpr59L9MkjLa/Y6HzDfM2ZZZu9L0L3err8iFBQUWJd3b1PXeu3tGD4+PphMJrvt1Wq1g6q36397q7f7tnbN0F69lgztdYoDrXegn40l47q6OusvEAP5bHqrt6/9pbcMu76nq74+m4HU27VTH2i9lrJ91Xst+3dcXJz1O93ftnbX37b6+vpiMBgUydBoNDr8vVGzj+gqMDDQ+sfIVX3EiaI6/rjvAgA//+Zkxo9osv4q3Ve9lm09fvk47YZ2ogKiSAxMRKPROKWP2DB/HJkFtRy6WMvTmQ384etRg/psuh/4g3P7iBBdCFPCp3C6+jTZLdnMC5035PuIrvUGBgb2+BVd+gizwfQRXesdPXq0zXvkOKJnvYP9bLrvw3Ic8eWywe7flv92zbiwsNAlfYQjHJotcN26dezcuZO6ujqbnWbXrl2sXLmSQ4cOMXv2bLtlFy9eTElJifUUosWmTZt4/PHHKSsr63EqHvqeLdDipZde4v777+eee+7h73//e58hyGyBQghx7do6DXzjz59wqbqZ2zNiefquDIf/8Pz26G/Zfn47d4y/g5/N/plT21d9tZ2bn/mYmqYONsxP5tGv9z9zoSs9d/o5tpzawsKEhfxp/p9c3RwhhBDdKDpb4NKlS2lqauL111+3eX3btm3ExsYyc+bMPsvm5OTYzCio1+vZvn07M2fOtDuwGoitW7dy//33s3r1al588UWnXF4ohBDCvj/uu8Cl6mYig3T84ptp19TnWiZwuDHuRmc3j4ggHb/6lvm+gb9+dIkzpfVOX4czzY0zT0F/pOIInUb7l7oIIYTwHA5dFnjzzTezaNEi1q9fT2NjI+PGjWPnzp3s3buX7du3W0/BrV27lm3btpGfn09iYiIA9913H5s3b2b58uVs2rSJyMhItmzZQm5uLvv377dZT1FREceOHQOw3iD52muvAeYb6qZPN0/b++qrr7J27VoyMjJ44IEHOHr0qE0906ZNs7lZUAghxLU7UVTHi59cAuCppVMICbB/aUZfSq+WUthYiFajZWZM7z/IDcaStBhunRrDO2cqePTVM/z74TnovO0/g9HVJoVNIlQXSl17HaeqTjEjeoarmySEEGIQHJ7Q4o033mDjxo088cQTXLlyhdTUVHbu3MmKFSus7zEYDBgMBptL+XQ6HQcOHOCxxx7j4YcfpqWlhYyMDPbs2cO8efNs1nHw4EHWrFlj85rl2Vr33HMPW7duBeDdd9/FaDTy+eefM2fOnB5tLSgo6DF7iTvKzc213q/QffYS4RySsTokZ+W5KuO2TgOPvnYaowmWTYtj4aSoa6rns/LPAEiPSCfIN8iZTbTx829O5nB+LbmXr/KXDy7yg8UDz0rNjL00XsyOm827l97lUNmhYTO4kr5CeZKxOiRn5Xlaxg7faBQYGMgzzzxDRUUF7e3tnD592mZgBeZL9UwmU4+BTVRUFNu2baO2tpbW1lYOHz7MwoULe6zj3nvvxWQy2f1nGVh1XU9v/zxhYAXmqUYt/4QyJGN1SM7Kc1XGf9pvvhwwIkjHE7dN6r9AL5S8JLCrsMAvLw/c8mE+WWUNAy6rdsZzYueg0+po1beqsj53IH2F8iRjdUjOyvO0jGUWBzeg1Wrx8vKyO7OJcA7JWB2Ss/JckfGFy1d58RPz81d+/a00Rgb49lOidwlBCcSMiLE+QFdJN0+J4ZapMRiMJja+mYXROLD5m9TOeHHSYg6tPMTjMx9XZX3uQPoK5UnG6pCcledpGTs0W+BQILMFCiHEwJlMJlb/PZNDF2tZPCmK5++e7pQ6wTnPN+xPVWMb83//Ic0dBn6/PJ1vXx/ffyEhhBDiC4rOFiiEEGJ4eT/7Mocu1uLr7cVPbrn2ywG70mg0qs3sGhnsx38tGA/Apj05XG1z7xn5WjpbXN0EIYQQgyCDKyGEEHa1dRr41bvnAFg3dywJYQGDqi+/Ph+D0eCMpjlkzZwxjA0fQU1TO89+cFH19Q/EpYZLLH1rKcv+vazP5zoKIYRwbzK4EkIIYdcLH1+itK6V6GA/HpyfPKi6Wjpb+Pa/v83cXXOpba11UgsHxtfbi5/eaj7r9tKhAvKrm1Rd/0BEB0RT2FhIeVM5lc2Vrm6OEEKIa+TwVOzC+aqqqjAYDGi1WiIjI13dnCFJMlaH5Kw8tTIur29l84fmszw/vmUiAb6D+3NR2FiIv7c/wbpgwvzDnNFEh8xPjeRrqZF8kFPFL985x9Y1X+n1va7YjwN8Avjrwr+SEprCSL+RqqzTlaSvUJ5krA7JWXmelrEMrtxARUWFdf5+T9hpPJFkrA7JWXlqZfyH/1ygrdPIV5JGcdvUmEHXNylsEp+s+ITLLZed0Lpr89NbJ/FJXjUf5lbzaV4NN44Pt/s+V+3HSj1U2R1JX6E8yVgdkrPyPC1juSxQCCGEjbzLV9l9shSAjbdMdNrkE1ovLbGBsU6p61qMCR/B6hsSAfjd+zlyb5MQQginkzNXbiApKQmTyaTa7FnDkWSsDslZeWpk/Pv/5GI0wdcnR5E+evCXqBlNRjSoN0NgXzbMH8crx0o4XdrA+9mVLEnreVbOlfvx9nPb2V+8nx9O/yFp4Wmqr18t0lcoTzJWh+SsPE/LWAZXbiAkJMTVTRjyJGN1SM7KUzrjUyX1vJ99GS8N/HBxilPq3Fe0jz8e/yPfGv8t1qevd0qd1yo8UMf9N47hzx9c5Pf/ucCiSdFovWz/YLtyPz5x+QQnLp/gUNmhIT24kr5CeZKxOiRn5XlaxnJZoBBCCKvfvZ8DwNJp8YyPCnJKnZkVmZQ3l9PY3uiU+gbr/q+OZWSADxermnjj81JXN8fGrNhZAByuOOzilgghhLgWMrgSQggBwKGLNRy6WIuPVsMjC8c7rd7MikzAfSZsCPbzYf0889TyT+/Po12v/rO3ejMrxjy4Ol19Wh4oLIQQHkgGV26go6PD+k8oQzJWh+SsPKUyNplM/L/3cwH4zsxERo8a3AODLSqaKii+WoxWo2V61HSn1OkM98xOIipYR1l9Kzsyi22WuXI/Hh08mrjAOPRGPccvH1d9/WqRvkJ5krE6JGfleVrGcs+VGzh//rx1isn09HRXN2dIkozVITkrT6mMP7pQzemSevx9tGyYP85p9R6pOALA5PDJBPoGOq3ewfLz0fJfC8azcXcWz32Yz8qvJODnowVcvx/fEHMDr+e9zuHyw3w1/quqr18Nrs54OJCM1SE5K8/TMpYzV0IIMcyZTCae/cD8wODvzEwgIkjntLozK7+4JDDaPS4J7Gr59aOJDfGj6mo7r55wn3uvLPddWQamQgghPIecuXIDISEh1idPC2VIxuqQnJWnRMZHLl3hRFEdvt5erPvqWKfVazKZ3O5+q658vb343k3JPPFWNn/9MJ8VM0bjo/Vy+X48M3omGjRcrL9IVUsVkQHu/9BMR7k64+FAMlaH5Kw8T8tYBlduICkpydVNGPIkY3VIzspTIuO/HMwDYMWM0UQG+zmt3ksNl6hprUGn1ZERmeG0ep3pzumjefaDi5TVt7L7ZBl3Th/t8v14pN9IJoVNIrs2myMVR/hm8jdd2h4luDrj4UAyVofkrDxPy1guCxRCiGHsRFEdhy7W4u2l4YEvZtBzFstlbRmRGei0zrvU0Jn8fLSsm2s+W7fl4EX0BqOLW2R2Q8wNABwulynZhRDCk8jgSgghhrG/fGA+a3XHdfHEjfR3at2WSwItAwV3tWpmAqEBPhTWtvDu2QpXNwewve/KZDK5uDVCCCEGSgZXQggxTGWVNXAwtxovDay/yblnrfRGPccrzVOJu+NkFl2N0Hmz9sYxAPzlg4sYja4fzFjO9tW01pBfn+/q5gghhBgguefKDeTn51unmExOdu4BjjCTjNUhOSvPmRk/96H5oP2b6bEkhY9wRvOsztee52rnVYJ8gpgUNsmpdSvh7tlJ/O3jS+RVNfHPg6eZGefn0v1Yp9VxXeR1HK44TGZlJuNCnTc9vjuQvkJ5krE6JGfleVrGMrhyA01NTdadRihDMlaH5Kw8Z2VcXNvCnizzJXDfc/JZK4CzNWcBmB49Ha2X+8/wFOznw/+5IZEtH+bzyqlqJoeEunw/fiD9Ab479bukR7j/c10cJX2F8iRjdUjOyvO0jGVwJYQQw9D/HirAaIJ5EyJIjQ52ev2rJq5i3uh5tOnbnF63Uu6dncQLn1ziXHUHF2o7mBzt2j/k10dd79L1CyGEcJzGNMzulDUajVy9etXmtaCgILy8XHf7mdH45exUrmzHUCYZq0NyVp4zMq5v6WDWbz6gtdPAy/fPZM64cGc1z+M9+uppXj1Rys1p0WxeNU32Y4VIX6E8yVgdkrPyXJ2xo2MH2QvcgJeXl/WfUIZkrA7JWXnOyPjlzGJaOw1MiglmdnKYE1vn+b77xUOU38+upKSu1cWtgbPVZ3kq8ylev/C6q5viVNJXKE8yVofkrDxPy9jhVjY1NfHII48QGxuLn58fGRkZ7Nq1a0Blq6qquPfeewkPDycgIIBZs2Zx4MCBHu975513uPvuu5kyZQo+Pj5oNJpe6+zs7OTnP/85SUlJ6HQ6UlNTefbZZx3dLCGEGBba9QZeOlQIwLqvju2zf71WL559kYcPPMyhskNOr1tpE6KCuCklAqMJ/vfTAlc3h3O159iZs5N3C951dVOEEEIMgMODq2XLlrFt2zaefPJJ9uzZw4wZM1i5ciU7duzos1x7ezsLFizgwIEDPPPMM7z11ltERUWxZMkSPvroI5v37t69myNHjjBp0iTS0/u+kffBBx/kN7/5DRs2bOD9999n6dKl/Pd//zdPPfWUo5smhBBD3lsny6lpaicmxI9bpsYoso6DJQf5sPRDqlqqFKlfaZaHCv/reCn1LR0ubcvsuNnclXIXd0+626XtEEIIMTAO3XP13nvvccstt7Bjxw5WrlxpfX3x4sVkZ2dTXFyMVmt/VqgtW7awYcMGPvvsM2bNMj8cUa/Xk56eTmBgIJmZmdb3Go1G66m/hx56iM2bN9t9iGJ2djZTpkzh17/+NY8//rj19XXr1rF9+3ZKS0sZNWqUTRl3vOeqtrbWus1hYXKJjhIkY3VIzsobTMZGo4nFT3/MxaomNn5jovUSOGc7V3uOw+WHuS35NiIDIhVZh5Jqamr4zj/OklvVwqNfT2HD/KE1Dbo7kL5CeZKxOiRn5bk6Y0Xvudq9ezeBgYEsX77c5vU1a9ZQXl5uM0CyVzYlJcU6sALw9vZm9erVHD16lLKysi8bNcCBzptvvonJZGLNmjU92tPa2srevXsHVI+rlZaWUlRURGlpqaubMmRJxuqQnJU3mIw/zqvmYlUTgTpv7vrKaAVaZzYpbBJrp6z1yIEVQFlZGUuSzJPpbv2skA69sZ8SwlHSVyhPMlaH5Kw8T8vYocFVVlYWEydOxNvbdgb3qVOnWpf3VdbyPntls7OzHWmKtc6IiAiio6Mdbo8QQgw3Wz8rBODO6aMJ9vOM54W4yqx4P0b5e1F9td36PDBX6TR28vnlz/lX7r9c2g4hhBD9c+g5V7W1tYwd2/MyEsuld7W1tX2W7X6J3kDLOlrniBEj8PX1HXCd2dnZJCYmEhz85bNe2tvbycnJASA0NJSEhASbMnl5ebS0tAD0uC+spqbGeiYuISGB0NBQ6zKDwWAd9AUFBTF27Fji4+OtpzsLCgpobGwEYPLkyTYD2fr6eoqKigCIjY0lIiLCZr1nzpzBZDLh7+/PhAkTbJaVlJRw5coVAFJSUvDz87Mua2pqIj8/H4DIyEhiYmzvwzh37pz14W2TJk2yWVZRUUFVlfm+iuTkZAIDA63L2trayM3NBcyf8+jRtr+UX7hwgdbWVjQaTY+Bd3V1NeXl5QAkJiYycuRI6zK9Xm8djAcHBzNmzBibspcuXbKevk1LS0Or1Vozbm1t5fTp0wDExcURHm47BbVlWUBAAOPHj7dZVlxcTF1dHQCpqanodDrrssbGRgoKzDe/R0VF9RjwZ2dno9frrZOudFVeXk51dTUA48aNY8SIEdZlLS0t5OXlARAWFkZ8fLxN2dzcXNra2tBqtaSlpdksq6qqoqLCfFCYlJRESEiIdVlHRwfnz58HICQkhKSkJJuy+fn5NDU1ATBlyhSbs8m1tbXWX4/i4+NtTtHHxcVRUlKC0WgkPz+/x5PUCwsLaWhoAGDixIn4+vpalzU0NFBYWAhATEwMkZG2Zz2ysrIwGAz4+fmRkpJis6y0tNT6fR8/fjwBAQHWZc3NzVy8eBGAiIgIYmNjbcrm5OTQ3t6Ot7c3kydPtllWWVnJ5cuXARgzZozL+oiudDodRqMRo9GIXq8fcB9xqbqJD3Or0QBzY3qeiXFWH7G/bT9jQsawIGEBAT4BHtNHWNTV1WE0GtH5ePOttHD+91gVLx0q5PaMOMA1fUROYQ73fHIPGjTcGHkjsaFf7sOe1kcYjUbOnj2L0WgkICCAqKgom3qljzAbTB9hOY4wGo3Ex8fbPHhVjiPMBttHFBcXA+a/eV2P4UCOIywG20cABAYGkpycbJOxK/oIy/d0oBx+iHBfM0v1N+vUYMoqWader+9xT5fJZKKzs9O63F4Zy/LujEajdVnXufktutfbdae6cuWKdXn3NnWt12Aw2K3XZDLZfYK1wWAYVL29bWvXertva9cM7dVrydDe5zTQegf62Vgyrq2ttXbiA/lsequ3r/2ltwz1er3dS177+mwGUm9nZ6fdZX3VaynbX7329LV/jxo1ytqx2SvftU3d9betHR0dGI1Gu/d1OiNDexkNtF6l+4iutFqtdTsc+S7/47D5gOq6GF+iAhzbDwfaR9R31vNC9gsAfHzXxwT4BHhMH9F1Wy1tufP6WLZ/XsOpknpOFtcxLSHUJX3ESJ+RxOpiKW8v50TVCZvBlaf1EV3rtXf/hPQRZoPpI7rWGxYWZnNMIMcRPesd7GfT/QBejiNs67VnoPt31/3Yor6+3iV9hCMcGlyFhYXZPRtk+SXD3lkkZ5Ttq85Tp071eL25uZmOjo4B1+nt7d3ji6nRaKydS/fLIC2v2et8wPwHw7LM3pdgoPV2b1PXeu3tGD4+PphMJrv1arXaQdXb9b+91dt9W7tmaK9ey7ba6xQHWq+7fDb9batlO/vL8FrqNRgMdpf1Va+lbF/1DjbD/ra1u/621dfXF4PBoEiGRqPR4e+NO+6HvX2Xr7Z18urxEgC+mRKsWB+R22j+hTl1VCqhfqE96vW0PiI8UMdt6bG8/nkp2z4rZFpCqMv6iLSgNMrbyzledZzbUm5zqF7pI6SPsFevHEe412cjxxE963WnPsIRDs0WuG7dOnbu3EldXZ3NTrNr1y5WrlzJoUOHmD17tt2yixcvpqSkxHoK0WLTpk08/vjjlJWV9TgVD33PFvjUU0+xceNGKioqbE6fHjlyhFmzZvHyyy+zatUqmzLuOFugEEIo6aVDBfz87XOMiwxk3/e/qsizrQCeOPQEuy/u5p5J9/DDGT9UZB1qO1vawG1/+RQfrYZD//drRAb79V9IAR8Uf8B/H/xvEoMTeWfpOy5pgxBCDEeKzha4dOlSmpqaeP112yfFb9u2jdjYWGbOnNln2ZycHJsZBfV6Pdu3b2fmzJl2B1b9uf3229FoNGzbts3m9a1bt+Lv78+SJUscrtMVLPdP2Ds1KpxDMlaH5Kw8RzM2Gk1s+2Iii3tnJyk2sAI4WnkUgJkxvf8t8ARdM54SH8L0xFA6DSZezix2WZtmRM/AS+NFUWMRlc2VLmuHs0hfoTzJWB2Ss/I8LWOHLgu8+eabWbRoEevXr6exsZFx48axc+dO9u7dy/bt262n4NauXcu2bdvIz88nMTERgPvuu4/NmzezfPlyNm3aRGRkJFu2bCE3N5f9+/fbrKeoqIhjx44BWG+QfO211wDzDXXTp08HzBM+rF27lieffBKtVsuMGTP4z3/+w/PPP8+vfvWra7rU0BXOnj1rvdGzv4cmi2sjGatDclaeoxl/dKGawtoWgvy8WXZdnGLtKrlaQllTGd4ab66Pul6x9aihe8b3zknieFEdL2cW8+D8ZHTe9p/nqKQg330x9y8AACAASURBVCDSwtI4U3OGIxVH+Na4b6neBmeSvkJ5krE6JGfleVrGDk9o8cYbb7Bx40aeeOIJrly5QmpqKjt37mTFihXW9xgMBgwGg82lfDqdjgMHDvDYY4/x8MMP09LSQkZGBnv27GHevHk26zh48GCPZ1dZnq11zz33sHXrVuvrW7ZsIS4ujmeffZbKykqSkpJ45plnePjhhx3dNCGEGHIs06+vmDGaAF+Hu/wBy6wwX5UwNWIqAT4B/bzbs3x9cjTRwX5UNrbx3tkKlk6L77+QAmbGzBwygyshhBiqHLrnaihwx3uu8vPzrSPy7lNXC+eQjNUhOSvPkYyLa1uY9/uDmEzw0aM3kRg2os/3D8ajHz3K3sK9rE9fz4MZDyq2HjXYy/jZA3n8Yd8Frk8M5fX19u8tVtrRiqOs/c9awv3D+WD5B4pe4qk06SuUJxmrQ3JWnqszdnTsoNzPmGLA5MuoPMlYHZKz8hzJ+OWjRZhM8NUJEYoOrIwm45C53wrsZ3zXjNE8cyCPE0V1nK9oZGJMsJ2SykqPTEen1VHTWsOlhkskj/Tc75v0FcqTjNUhOSvP0zKWKfKEEGIIatcbePW4+SGNq2cm9PPuwcmry+NK2xX8vf2ZGj61/wIeKDLYj8WTzQ+83X6kyCVt0Gl1TIucBsCRiiMuaYMQQoi+yeBKCCGGoL1ZlVxp7iAmxI+vpUb2X2AQLPdbXRd1HT5a+88fGQpWzzRP0PTmyTKa2ns+IFQNN8TcAMjgSggh3JUMroQQYgiynF1ZMSMBb62yXX1mpXlwdUP0DYqux9VmJYcxNnwEzR0G3jxZ5pI2WAZXxyuPoze6ZoAnhBCid3LPlRsoLCy0Ph07KSnJ1c0ZkiRjdUjOyhtIxjmVjRwrrEPrpWHFV0Yr2p5OYyfHK48DQ+N+K+g9Y41Gw6qZCfzq3fNsP1LEd2YmqD6pROqoVObEzmFKxBQ6DB14e3nmn3HpK5QnGatDclaep2Xsmb3yENPQ0GCdBUUoQzJWh+SsvIFkvOOLh90unhRFVLCfou0xmoz86Cs/4nT1aVJGpSi6LrX0lfG3r4/nd+/nklN5lc+L67g+Ud3nKWq9tPx10V9VXacSpK9QnmSsDslZeZ6WsVwWKIQQQ0hzu543Pjdfsrb6hkTF16fT6lg6fik/m/0zvDRD/0/KyABfbkuPBeDlI8Uubo0QQgh3I8+5wvXPuero6LD+v6+vr8vaMZRJxuqQnJXXX8Y7Mov58e6zjAkfwYH/mYeXl+c+C8lV+sv4VEk939p8CF9vLzIfX0DoCPX39Yb2Bo5XHmdO3Bz8vJU9O6kE6SuUJxmrQ3JWnqszdnTsMPR/ZvQAvr6+1n9CGZKxOiRn5fWVsclksk5k8Z2ZCYoPrFr1rfzz3D+5UHeBofQ7XX/7cXp8CGlxwXTojbx6okTl1pnd+fadPPLhI3xe9blL1j9Y0lcoTzJWh+SsPE/LWAZXQggxRJwqqedcRSO+3l58+/p4xdd38vJJ/t+x/8eGAxsUX5c70Wg0fOeLadlfzizGaFR/YDk9ejpjQsbQpm9Tfd1CCCF6JxNaCCHEELH9i3uAbp0aw8gA5X/h89H6MCd2DqODRqs+a56r3Z4Ry1PvnqeotoVD+TXMHR+h6vp/Nvtn+Hh5xs3dQggxnMjgyg00NDRgMpnQaDSEhIS4ujlDkmSsDslZeb1l3NDSyTtnygF1JrIAmBE9gxnRM1RZl5oGsh8H+Hqz7Lo4th0uYvuRItUHV54+sJK+QnmSsTokZ+V5WsYyuHIDhYWF1ikm09PTXd2cIUkyVofkrLzeMn7zVBnteiOp0UFMGz3ShS30fAPdj1fNTGTb4SIOnK+i6mobkUHqTyzRaeikRd9CiO6LA472JricDVcuQdPlL/5VgeHLG8LR+sCISAiMhKBoCB0D0WmgC1Kt3dJXKE8yVofkrDxPy1gGV0II4eFMJhM7j5ovCVz5FXUebFvRVIHWS0tkQKTi63JXKdFBTEsYycniel4/Ucb6m5JVXf+unF388fjv+WbIRH7S7gsVp6A2H7jGe8BGjYWYdBgzD8YvghDl79sTQoihRgZXbiAmJsb65GmhDMlYHZKz8uxlfLasgZzKq/h6e/GtjDhV2vH3rL/zSu4rPJjxIOvT16uyTrU4sh+vnJHAyeJ6XjlWzPfmjVXn3rPafDi9i8iLb9Gqayez8hiUVXy5PCgGIlLM/w2MNJ+l8tZ9udzQYT6b1VQFVyugOheulpvPdl25BNm7ze+LmAgpSyB9FURMcOomSF+hPMlYHZKz8jwtYxlcuYHIyOH7y69aJGN1SM7Ks5fxrmPm6cC/kRZNSIA69+JkVmQCMCHUuQfd7sCR/fiWqTH8/O1sCmtbOHLpCrOSw5RpVEczZL0Op3ZA8WEApntp8EqIp9DXh8o5DxE9Zj5ETzUPqBzVXAOVZ6D0OFzcD6XHoPq8+d+nf4K46ZCxCqbe6ZTLB6WvUJ5krA7JWXmelrFMxS6EEB6spUPPv0+ZJ7K4a0aCKuu83HyZwsZCvDReQ3JCC0eM0HnzzS/OFr5yrNj5K2iuhYO/gT+lwb8fNg+sNF4wbhHBt/+NyaMmAXBkzAwYt/DaBlYAI8Ih+Wsw7zFY+x94NB/u+DtMuBk0Wig7Du/+D/xpMhz4hfmslxBCiB5kcCWEEB7s3TMVNLXrSQoL4Iaxo1RZZ2al+azVpFGTCPYNVmWd7mzFjNEAvJdVSX1LRz/vHqDmGtjzI3g6DT7aBK1XIDQJFv4cvn8OVr8G6XdxQ/yNwJdnEp0mYBRM+Tas2gU/yIHFv4awcdDWAJ/8AZ6eAu/+AK5edu56hRDCw8ngSgghPNgrX1wSeOcM9Z41ZTmQnxkzU5X1ubup8SFMjAmmQ2/kzZNlg6uss9U8eHkmAzKfg84W8yQT334JHv4cbnwEgmOsb7d8BpkVmZhMCj3MODASZj8EG47BXdvNlwjq2+DYi/DnafDhJvMshUIIIeSeK3eQlZVFR0cHvr6+pKWlubo5Q5JkrA7JWXn/n73zjo+qyvv/e2YyaaSQTnoCJPQmNZSls3QFRUBEcFFcdd0Hfday67Ou+7D7qM/zW5UtoKIoC9JEEKSIEooIhiISSCD0kE56b9N+f1xmyCSTMmRqOO/Xi1eGe+/5nu/9zMnJ/d5zzvc01NgtKJozt0pQyGU88oBtMrvpdDqScpOAjhtcmduOZTIZC4ZG8qfdqWw5ncmSkTHmB7o6nbSm6rs3oPxOgBY6ACa9CV3HQzP2BgYPxE3hRkFNATfKbtCtsxUzFsrl0GsW9JwJt47DwTeltVlH3oIz6yRfByxs1teGiL7C+giNbYPQ2fo4m8Zi5MoB0Gg0aLVaNBqNvV3psAiNbYPQ2fo01Fg/ajWhZzDBPrbZY+lm+U3yq/NxlbsyKHiQTeq0NffSjh8aGI6bi5y0vAqSs8rMq7A0Az6fB18ukwIr30iYuxaePiKtg2ohWHFTuDEweCCAIei1OjIZxIyGZd/BvM+k6YqVt+GrZ+HfD0oZB1tB9BXWR2hsG4TO1sfZNBbBlQPg7u5u+CewDkJj2yB0tj56feVKN3bcmYKmX/NjC/RTAgcGD8TdpWN+z/fSjn09lczoJ03X23KqjYkttFr4cTX8awRc+w4UrjDu9/CbM1JWPnnb/kSPCB0BWGHdVWvIZNBnDjx/Shq1cnGHm0dhdYKUYVCjbrao6Cusj9DYNgidrY+zaSzTWW2StmOi1WqpqKgwOubt7Y28jX/EBAKBwBHYez6X5zedJcTHjeOvTsBFYZs+bMXhFSRmJPLCoBdY3n+5Tep0Fk7eKGL+R0l4uio49fokvNxamHlflg07n4H0Y9L/o0bCrFX3tJ9USmEKC/cuxEvpxbEFx3CR22nGf/EN+HqFFGABRI6AuR+BX7R9/BEIBAILYG7sICIKgUAgcEK23En7PW9wpM0CK41Ww6m8U0DHXW/VHobF+tM1sBPV9Rr2JOc0f+HF3bBmpBRYKT1hxruwdO89b9Tby78X3q7eVKoquVh08R69twD+XeGJXfDganD1hswk+GA0nP/Cfj4JBAKBjRHBlUAgEDgZmcXV/HCtEIBHh9huSmBacRoV9RV0UnaiT0Afm9XrLMhkMubfmaKp39jZCHUd7HkRti2G2lIIHQjPHIOhy9o8BdAUCrmCYV2GAXaYGtgYmQwGLYJnf4DI4VBXDjuegp3PSpkQBQKBoIMjgiuBQCBwMr74KQudDkZ1DyAqwNNm9eoTJgztMtR+U88cnIcHR+Ail3Eus5S0vPK7J8qy4dPpUlY9ZDD6RSkhRGB3i9Q7PHQ4LjIXimuLLWKv3fjFwNJ90hoymRySN8EnU6Dklr09EwgEAqtidnBVWVnJihUrCAsLw93dnYEDB7Jly5Y2lc3Pz2fp0qUEBgbi6elJQkICiYmJJq89ePAgCQkJeHp6EhgYyNKlS8nPb7oj/LVr11i8eDFRUVF4eHjQrVs3XnrpJYqKisy9NbuRlZXFrVu3yMrKsrcrHRahsW0QOlufWxmZbE66CcD8oVE2rVsukxPkEWRIoNBRaU87DvRyY3LvEAC2nLozepX+A3w0FrLPgHtnaQPgSW+Ci6vFfJ7dbTbHFx7n1WGvWsxmu1G4wLjX4Ind4BkIeeclHa4fEn2FDRAa2wahs/VxNo3NDq7mzp3L+vXr+dOf/sT+/fsZOnQoCxcuZNOmTS2Wq6urY+LEiSQmJrJq1Sp27dpFSEgIU6dO5ejRo0bXHj16lGnTphESEsKuXbtYtWoVBw8eZOLEidTV1RmuKygoYMSIERw/fpyVK1eyb98+nn/+edauXcukSZPQarXm3p5dKCoqoqCgwKkCQmdDaGwbhM7WJzE1m4IqNd6ucqbceYi3FU/2fZLEeYk8Gv+oTeu1Ne1txwuGSUHvzp+zUZ38BNbPhqoCCOkHy49A90mWc/YOnZSd8FTabhTTLGLHwDNHIewBqCmBjQ8jO7mGgvx80VdYEdEf2wahs/VxNo3Nmtexb98+vvvuOzZt2sTChQsBGD9+PLdu3eLll19m/vz5KBQKk2U/+eQTUlJSOHHiBAkJCYayAwYM4JVXXuHkybvzxF9++WXi4+PZvn07Li6Si7GxsYwaNYp169bx7LPPArBr1y6KiorYunUrEydONNisq6vjD3/4A8nJyQwa1DH3YREIBPcn312vBmBcjCfuStP9rTWRyWQoFUqb1+tMjO4eSISvG49XfYpy/x7pYL95MOvv4Gr9AEilVaGUO9h35BsBT+6Hff8JP28k/MI/canIIm/Ab+3tmUAgEFgUs4KrnTt34uXlxbx584yOP/nkkzz22GOcPHmSkSNHNlu2R48ehsAKwMXFhccff5w//OEPZGdnEx4eTnZ2NqdPn+att94yBFYAI0eOJD4+np07dxqCK6VS+uPh6+trVFfnzp0BnCYfflxcHDqdDlkbdrUX3BtCY9sgdLYuBRV1nM6pBWDZ+F42rbuopgg/dz/kso6/VLe97VihqeVTr38RV3dIOjD+dfjFyy1uBmwJLhZd5M8//hmFTMGmGS3PJrELSneY/U8I7AHf/ZGQ9K8IlFdC7/Xg5mVv7zocoj+2DUJn6+NsGpsVXKWkpNCrVy+joAegf//+hvPNBVcpKSmMGTOmyXF92dTUVMLDw0lJSTE63vja48ePG/7/0EMPERUVxX/+53+yevVqoqOjOXv2LG+//TazZs2iV6+2PXykpqYSHR2Nj4+P4VhdXR1paWkA+Pn5ERVlvLbh6tWrVFdLb5AHDBhgdK6wsJDsbGlzz6ioKPz8/AznNBqN4R69vb3p2rUrnp5332TevHmT8nJpEXSfPn2MtC4tLeXWLWkxcFhYGEFBQUb1nj9/Hp1Oh4eHB/Hxxil9MzMzKS6WFjr36NHDKPCsrKzk+vXrAAQHBxMaGmpU9uLFi6hUKpRKJb179zY6l5uba1gL161bN7y87v6BrK2t5fLlywD4+/sTGWmc1ezKlSvU1NQgk8mafN8FBQXk5EipjKOjow0BM4BarSY1NRUAHx8fYmNjjcreuHHDsB9B3759USgUBo1LSkq4evUqAOHh4QQGBhqVTU5OBsDT05O4uDijcxkZGZSUlADQs2dP3NzcDOfKy8u5eVNaBxMSEkKXLl2MyqampqJWq3Fzc6Nnz55G53JycigoKACge/fudOrUyXCuurra4G9AQAARERFGZS9fvkxtbS0KhYK+ffsancvPzyc3NxeAmJgYo5cQ9fX1XLp0CZBeTsTExBiVvX79OpWVlQD069fPaC+HoqIiw7zniIgIAgICDOfc3d25cOECAF5eXnTr1s3Ibnp6OmVlZQD06tULV9e7a07KyspIT08HIDQ0lODgYKOyKSkpaDQa3N3d6dGjh9G5rKwsw3SBuLg4o9+pqqoqrl27BkBQUBBhYWFGZdPS0qirq8PFxYU+fYwz4OXl5XH79m1AGj23Vx+hZ8fZLNRaHfEBrsjKc1Gr/W3WRzy570mKVEW8MfANftnnl0ZlO0IfoaekpISMDCnNfXh4uFFbgtb7iPLbt4j98VXiilOp07nwimo5L/Z5Hv+KCqv3EbpOOi4WXUQuk1NRX4G3q7fD9RFanY4LXmPxHfbfRP30VxQ3DsJn02HRl+AVJPqIO9xrHwHiOUKPrfoI8Rxh4T5Cq23yHNHw99UefYT+97StmBVcFRUVNfklBqnB68+3VFZ/XUtl9T+bu7ZhHb6+viQlJfHwww8bNYh58+axYcOGttwSIP2SNd5LWafToVKpDOdNldGfb4xWqzWcM7Xuq612G/vU0K5GozFpV6fTGUb0GqLRaNplt7l7bWi38b021NCUXf29mnoT0Va7jvLdtHavKpUKtVptcsO5lr6btthVqVQmz7VkV1+2NbumaKuGpso39Kkxrd1rfX09Wq3W5NRjS2hoSqO22rVFO9TpdGy9k957QoybSZ+t1UdU11eTW5dLrbaWELem67xEH3Gn3vIcun7/Ap4VN9G5d+Zvvn9k161Qws9k8kxCqNX7iCBlEO+Pe59+Qf3wdvU22HXEPqIweBRMWE3M8VchNxk+nQqLd4o+4g7iOQJDPR2pjxDPERLO+BxhDmbn0m1pSK614TpzyjZ3bcPjJSUlPPjgg1RXV/P5558TGRlJSkoKK1euZPbs2ezdu7fJKJspXFxcTNav71xM2XBxcTHZ+QDI5XLDOVO/BG2129inhnZNNQylUolOpzNpV6FQtMtuw5/N2W18rw01NGVXf6+mvuu22nWU76a1e9XfZ2sa3otdjUZj8lxLdvVlW7LbXg1bu9fGtHavrq6uaDQaq2io1WrN/r2xdTs8nV7CjcIq3F1kjI31RqmU26yP8HT15IO+H5Bek05Ip6bBlegjgOIbhH/zK1wqs1G5B6J7fAcPlAbDrbNs/ymLp0aE2qSPmBgxsYldR+0jNH6DYNm38O+HoOgarJuK+4R/olQGNClj6l4bc7/3EabsiucIB+ojEM8RepzxOcIcZDozwrGEhAQ0Gg2nTp0yOp6amkrfvn358MMPWb58ucmyoaGhjBkzhm3bthkd37t3LzNnzuTAgQNMmTKFAwcOMHXqVPbu3cv06dONrp03bx7Hjx83DPO+9tprvPvuu9y6dctoCPrw4cNMmDCBzz77jCVLlhjZ0Gq1hqFePd7e3ia/XFtRVVVlmEvacChXYDmExrZB6Gw9Xtp2jh1ns3l4YBf+PLOH0NiKmN2Ob1+EDQ9B5W3wi4UnvgK/GOrVWka+nUhhZT0fPzGESTbO7ujIGGmsLoUNc6DwMnj4w+IdECaSUbUX0R/bBqGz9bG3xubGDmZFFP369ePSpUtNhjr1cyMbz9VsXFZ/XUtl9T+bu7ZhHefOnSM8PLzJ3N6hQ4cCGOYkOzrXrl0jLS3NMOdbYHmExrZB6GwdympU7LsgzXsfHqQRGlsZs9px3gVYP1MKrEL6wq8OSBvoAq4ucuY+IK1v2HJnSqctWJ+6nme+e4bbVbdtVqe5GGnsGy5lEgwbBDXF8O8HIedne7vo9Ij+2DYIna2Ps2lsVnA1Z84cKisr+fLLL42Or1+/nrCwMIYPH95i2bS0NKOU62q1mo0bNzJ8+HDDAtLw8HCGDRvGxo0bjeZLJiUlcfnyZebOnWs4FhYWRlZWlmHRp54ff/wRoMmiPYFAIHBGdifnUKvSEh/iRXyA5TaebQu5lbnM2jmLd069Y/a88w5P7nlpD6vqIikwWLoHvI1Hpx4dIi3AP3w5n9vltTZx60D6AU7knOBk3snWL3YUOgVImw1HDofaMmmqYM45e3slEAgEZqN4880332zrxXFxcZw4cYK1a9fi7+9PeXk5b731Ftu2bWPNmjWGbDfLli3j4YcfZsmSJYbsLP3792fnzp1s3LiRkJAQbt++zSuvvMKJEyfYsGGDUZaRuLg43nvvPZKTkwkICCApKYlnnnmGqKgo1qxZY5jHGhERwbp169izZw/e3t4UFxezZ88eVqxYgZeXFx988EGTTE86nY76+nqjY25ubnZN76jVavH09MTLywtvb2+7+dGRERrbBqGzdXh95wXyK+p4bnx3Bkb42lTjg7cOsvPaTmQyGQ/HP2z1+hyBNrXjnHOw4UFpU9zwwbB4J3j4NbnMv5Mrx68VklVSg5+nK8NimyZrsjRZlVmczT+Ll9KLiVETWy9gB0xq7OIGvR+E9ONQfB1Sv4JuE8C7S8vGBCYR/bFtEDpbH3trbG7sYHZCix07dvD666/zxhtvUFxcTM+ePdm8eTMLFiwwXKPRaNBoNEZvOd3c3EhMTOSVV17hhRdeoLq6moEDB7J//37Gjh1rVMe4cePYt28fb7zxBrNmzcLT05OZM2fyf//3f0ZpKwcPHkxSUhIrV67k9ddfp6CggPDwcGbPns0bb7zRJD2mo9I47avA8giNbYPQ2fKkZJeRkl2Oq0LOnEHh+Hey7chVUm4SACNCR9i0XnvSajvOS5GmrtWWQvgQaY2Qu2+zlz86JJLT6SVsO5PJc+O6Wf1l3vDQ4Xx84WOScpIcdm+YZjV294HHv4SNcyHrtKTzE7shtOn2LIKWEf2xbRA6Wx9n09ishBYdAUdMaCEQCATN8cevUtiQdIuZ/UP552MP2LRunU7HuG3jKK4t5tNffsqQLkNsWr9DUngNPp0GVfkQMRQe3yEFBC1QXa9m2F8TqaxTs/npESR0M50Nz1LUaeoYtXkUdZo6dj20i66+TbdQcXhqy2DDXMg+I40IigBLIBDYCasmtBAIBAKB7aip1/DVOWlN6fyhka1cbXmull6luLYYDxcPBgQNaL1AR6c0UxpJqcqHkH6waHurgRWAp6sLswdKb163ns6wtpe4KdwYGDwQgJO5TrTuqiHuvtKIYPgQaerlhoeg4Iq9vRIIBIJWEcGVQCAQOCj7U3KpqFUT4efBqG62n+aclCNNCRwcMhilwvS+IvcNlflSYFWeBQFxd9ZYdW5z8fl3ElvsS8mjrNr0BpiWRD+NU/8dOiX6ACtskJQ0ZMMcKMuyt1cCgUDQImavuRJYnrS0NFQqFUqlkp49e9rbnQ6J0Ng2CJ0tiz599/whkcjl0roZW2p8P663AhMa15RID/bF18E3StrHyivILJv9I3zp2cWbtLwKdiVn80RCjHWcv8OI0BGsYhWnb59Go9WgkDfdUNOetLkdu/tKI4TrpkLRVel7ePIbKbugoEVEf2wbhM7Wx9k0FiNXDkBdXZ3hn8A6CI1tg9DZctwoqOTUzWLkMnhkyN1tJWylsUqr4sztM8D9F1wZaVxXCRsfgdsp4BUiBVa+5m/zIZPJWHBnaufmU5lWT2vfy78X3q7eVNRXcKn4klXruhfMasedAiXdfSKg8Ap8/gjUVbRe7j5H9Me2QehsfZxNYxFcOQAuLi6GfwLrIDS2DUJny7H1jDRqNa5HMKG+HobjttL4QsEFatQ1+Lv7E+cXZ9W6HA2DxnJg2xN3kyos/goCut2z3YcGhePqIudSbjkp2eWWc9gECrmCoSFDgbsjkI6E2e3YN+LOVEx/yDkLWx8HtXM8aNkL0R/bBqGz9XE2jZ3Dyw5Onz597O1Ch0dobBuEzpZBpdHy5U/S2pLGiSxspfGPudJm7MO6DEMuu7/ew/Xp0wd0Otj1G7ieCEpPaWpaSO922e3s6crUPl3YnZzDltMZ9IvoZyGPTTM8dDiHMg+RlJvEU/2esmpd5nJP7TgoHh7fLm3cfOMI7HgaHvkUHGzKo6Mg+mPbIHS2Ps6m8f31F1MgEAicgMRL+RRW1hPo5caEnsF28eFE9gkARoaNtEv9dufIW3BuI8jk0gN8hGXS0OunBu4+l0NNvcYiNptjRJg0nfNc/jnqNB1klCd8MCz4HBSucHEXHPiDvT0SCAQCI0RwJRAIBA6GPl33I4MjUCps302X1pZyofACcJ8GVz+th6PvSJ9nvAs9plrM9IiuAUT5e1JRp2bfhVyL2TVFrE8swR7B1GnqOJd/zqp12ZSu42DuR9Lnkx9A0hp7eiMQCARGiOBKIBAIHIic0hqOXikA7LO3FcBPt39Ch47unbsT0inELj7YjSvfwp4Xpc+/eBmGPGlR83K5jEfvJCjZeicbpLWQyWT8bujvWDNpDf2DOtgGvH3mwOSV0udvfg+XvravPwKBQHAHsebKAcjLy0Oj0aBQKOjSpYu93emQCI1tg9C5/Wz/KQutDobH+hMb2KnJeVtoPCFqArse2kVJbYlV7Dss2WfhiyWg01AV9xAVvZZhDYUfGRzJu99d4VR6MTcKKuka5GWFWiSmxU6zmu32YJF2PPIFKEmHM5/Al0/D0j0Wm77ZERD9sW0QOlsfZ9NYjFw5ALdv3yY3N5fbt2/b25UOi9DYNgid24dWqzOMZiwcFmXyGltoLJPJ6OrblcEhg61Wh8NRlgWbF4CqmorgIaTFPcvt/HyrVNXF8WLh6wAAIABJREFU153xPaS1dPqskPcbFmnHMhlM+1+ImwLqGtg0H4pvWs5JJ0f0x7ZB6Gx9nE1jEVwJBAKBg3D8eiHZpTX4uLswta/jv53rMNRXSYFV5W0I7kP6sJXo5Nad2KGf8vnlT1moNFqr1vVz/s+8e+ZdTuedtmo9dkHhIiUc6dIfqgvh83lQXWxvrwQCwX2MmBboAMTGxqLT6ZDJZPZ2pcMiNLYNQuf2seXOqNWcQeG4K02nl7a2xtsub+Nk7kkejnuYkeH3QTILrRZ2LIe8C9ApCB7bQrS8s9Xb8fiewQR6uVFYWUfipXyrBtN7b+xl6+Wt1KhrGNplqNXqMQeLtmM3L3hsG3w8CYquSnuTLd4JCmX7bTsxoj+2DUJn6+NsGovgygHw8fGxtwsdHqGxbRA63zvFVfV8m5oHwPyhpqcEgvU1/u7WdyTlJjEoeND9EVwd/guk7ZFSe8//HDpHYYtWrFTIeWRwBB8cvc62M5lWDa4mRE2gTlPHmIgxVqvDXCzejn1CYdE2+GQKpB+D/a/CzHctW4eTIfpj2yB0tj7OprGYFigQCAQOwI6zWag0OvpH+NI7zH5/SH476Lc8O+BZxkaMtZsPNiN5Kxz7m/R59j8garhNq9dPDTxyOZ/cshqr1TMybCQrR63kFxG/sFodDkFIH5i7FpBJSS5Of2xvjwQCwX2ICK4EAoHAzuh0dxNZ2Cv9up5+Qf14buBzRPrY1w+rk3kKdv9G+jz6RRiwwOYuxAZ2YlisP1odbD+TZfP6OyQ9p8PEN6TP+16Bm9/b1x+BQHDfIYIrB6Curo7a2lrq6urs7UqHRWhsG4TO98bZjFKu5lfioVQwe0BYi9cKjS1AaQZseQw09dBzJkx4w+i0LTVecCeY3nomE61WZ7V6tDotqUWpJGYkWq0Oc7CqxqNfhH6Pgk4jrb8qvmH5OpwA0VfYBqGz9XE2jcWaKwcgLS0NlUqFUqlkwIAB9nanQyI0tg1C53tj6+kMAGb0D8XbveVF+NbU+B8//4Ne/r0YEzEGN4WbRW07DHWVsHkhVBVASD+Y8yHIjd8z2rIdT+sbyp92p5JVUsOPN4oY1T3QKvWcvX2WJw88ib+7P+MjxyOX2ffdqlU1lslg9t+h6BrknJW+72XfgbtzrdtoL6I/tg1CZ+vjbBqLkSuBQCCwIxW1Kr5OzgXujmLYg5zKHD46/xG/O/o76jTO8XbQbPSZAW+nQKdgWLhZyjRnRzxcFTw0MBy4my3SGgwIHkAnZSeKa4u5WHTRavU4DEoPWLAJvEOhIA12PA1ajb29EggE9wEiuHIA/Pz88Pf3x8/Pz96udFiExrZB6Gw+e87nUqPS0C2oE4OjW9fNWhofzzkOQL/Afvi4dtA3/D/8DS7vlTIDLvgcOpsOZm3djvXr7A6k5FFSVW+VOpRyJSNCRwBwLPuYVeowB5to7BMqfc8u7nDlG0j8b+vV5YCI/tg2CJ2tj7NpLKYFOgBRUc2nXRZYBqGxbRA6m49+tGLB0Kg27eFhLY1PZJ8AYFT4KKvYtzvXDsKhv0qfZ/wNIoc1e6mt23HfcF/6hPmQmlPOzp+z+dXoWKvUMzp8NIkZifyQ/QPPDnjWKnW0FZtpHD4YZv8TdjwFx9+H4N4wYL5t6rYzoj+2DUJn6+NsGouRK4FAILATl3LLSc4sRamQMeeBcLv5odaqOZl7EoBRYR0wuCq5BV8+BejggSXwwBP29qgJhsQWpzPR6ayT2GJ0+GgALhRcoLS21Cp1OCT958Hol6TPX/8WcpPt649AIOjQiOBKIBAI7IQ+/frk3iEEetkvgcSFwgtUqCrwdfOld0Bvu/lhFVQ1sG0x1JRA2CCY9r/29sgksweG4+Yi5/LtCs5lWifw6dKpC907d0eHjh9zf7RKHQ7LhD9C3BRQ18LWx6G62N4eCQSCDooIrgQCgcAO1Ko07Dgr7W00f6h9pzwcz5bWW40MHYlCrrCrLxZFp4O9v5NGKjz84dENoHS3t1cm8fVQMr1fKACbT2VYrZ4x4WMA+CH7B6vV4ZDI5TD3I/CLlVLxb/+VSHAhEAisggiuHICrV69y6dIlrl69am9XOixCY9sgdG47e87nUl6rJtLfgzFmpN+2hsYncqT1ViPDR1rMpkPw02dwbiPI5PDIumYTWDTGXu140XApyP46OZeyGpVV6tBPDfwh+we0Oq1V6mgLdtHYww/mbwSlJ9w4DIf+Yru67YDoj22D0Nn6OJvGZgdXlZWVrFixgrCwMNzd3Rk4cCBbtmxpU9n8/HyWLl1KYGAgnp6eJCQkkJhoekPDgwcPkpCQgKenJ4GBgSxdupT8/HyT16akpDBv3jyCgoJwc3MjJiaG5557ztxbsxvV1dVUVVVRXV1tb1c6LEJj2yB0bjufn7wFwMJhUcjlrSey0GNpjQtrCkkpTAE62HqrrJ9g/yvS5wl/hG7j21zUXu14cLQf8SFe1Kg0fPVztlXqGBQ8CE8XT4pri7lUfMkqdbQFu/UVXfrC7H9In394Fy7utm39NkT0x7ZB6Gx9nE1js4OruXPnsn79ev70pz+xf/9+hg4dysKFC9m0aVOL5erq6pg4cSKJiYmsWrWKXbt2ERISwtSpUzl69KjRtUePHmXatGmEhISwa9cuVq1axcGDB5k4cWKT3ZkPHz7MsGHDKC8v54MPPuDbb79l5cqVuLs75tQPgUAguJhTzs8ZpbjIZcwbbL+9rUAawdCho3dAb4I8g+zqi8WoKoRtT4CmHnrOhNEv2tujNiGTyVg0PBqATSczrJLYQqlQMjx0OAA/ZN1nUwP19HsERjwvff7qWSi4bF9/BAJBh0KmM6P33rdvHzNmzGDTpk0sXLjQcHzKlCmkpqaSkZGBQmF6vv7q1at5/vnnOXHiBAkJCQCo1WoGDBiAl5cXJ0+eNFw7bNgwqqqqSE5OxsVFyhZ/4sQJRo0axerVq3n2WSmFbHV1Nd27d+eBBx7g66+/blMaY61WS0VFhdExb29v5HIxQ1IgENiG//rqAhuTMpjRP5R/PfaAXX156chLfHfrO3494Nc8P/B5u/piETRq2DgHbn4PAd3h6UPg7mtvr9pMWY2K4f9zkFqVlu2/TmBIjL/F69h2eRsrk1YyMGggG6ZvsLh9p0Cjhg0PQfoxCIi700466P5uAoGgXZgbO5gVUezcuRMvLy/mzZtndPzJJ58kJyfHKEAyVbZHjx6GwArAxcWFxx9/nFOnTpGdLU2ByM7O5vTp0yxevNgQWAGMHDmS+Ph4du7caTj2xRdfkJuby8svv9ymwEogEAjsTVWdmq9+zgFg0TD7JrJQaVSG9Va/CP+FXX2xGIdWSoGVspO0vsaJAiuQElvMHhAGSKNX1kCf1OJ84XnK6sqsUofDo3CBRz4F7zAouiqNYGnttwZNIBB0HMzaRDglJYVevXoZBT0A/fv3N5wfOdL0guiUlBTGjBnT5Li+bGpqKuHh4aSkpBgdb3zt8ePHDf///vvvAdBoNIwePZpTp07RqVMnpk6dyt/+9jfCwsLadF+pqalER0fj43P3rVVdXR1paWmAtDN04w3Mrl69apj7OWDAAKNzhYWFhmAxKirKaEdpjUZjuEdvb2+6du1qVPbmzZuUl5cD0KdPHyOtS0tLuXVLWqcRFhZGUJDxFJ7z58+j0+nw8PAgPj7e6FxmZibFxVLq2R49ehhNm6ysrOT69esABAcHExoaalT24sWLqFQqlEolvXsbp2nOzc01rIXr1q0bXl5ehnO1tbVcvixNt/D39ycy0nj605UrV6ipqUEmkzX5vgsKCsjJkR5Ao6Oj6dy5s+GcWq0mNTUVAB8fH2JjjTfcvHHjhuENQ9++fY1GU0tKSsjIkB5YwsPDCQw0TiSQnCztf+Lp6UlcXJzRuYyMDEpKSgDo2bMnbm53U2eXl5dz8+ZNAEJCQujSpYtR2dTUVNRqNW5ubvTs2dPoXE5ODgUFBQB0796dTp06Gc5VV1cbFnAGBAQQERFhVPby5cvU1taiUCjo27ev0bn8/Hxyc3MBiImJwdf37kNmfX09ly5J6y18fX2JiYkxKnv9+nUqKysB6Nevn9HbmaKiIrKypCx3ERERBAQEGM5ptVouXLgAgJeXF926dTOym56eTlmZ9DDXq1cvXF1dDefKyspIT08HIDQ0lODgYKOyKSkpaDQa3N3d6dGjh9G5rKwsioqKAIiLi8PT09NwrqqqimvXrgEQFBTUpF9IS0ujrq4OFxcX+vTpY3QuLy+P27dvAxAbG2uRPmJ3cg6VdWrCvF3wrMyipERhtz7ibP5ZqlRV+Lv741PjY2j/TttHXNwtbRQL3Br4O0pz6/Gpuul0fcRjw6PZdiaLPRdy+ePM3tSUFVq0jwj1CmVy9GQCFYEkX0jGV+l7f/YRXkEwfyO6T6ciS9tD7vZX0I1+ye59BIjnCD3iOeIu4jlCwh7PEeau9TIruCoqKmrySwxSg9efb6ms/rqWyup/Nndtwzr0Hc/DDz/M8uXLWblyJVeuXOH1119n7NixJCcnG4nTHGq1usncdp1Oh0qlMpw3VUZ/vjFardZwTmviTVhb7Tb2qaFdjaZpClmVSoVOp0OpVDY5p9Fo2mW3uXttaLfxvTbU0JRd/b2aGnVsq11H+W5au1eVSoVarTY5hNzSd9MWuyqVyuS5luzqy7Zm1xRt1dBU+YY+Naa1e62vr0er1ZqcemwJDU1p1Fa7bW2HOp2OjUnSg82kWHfUarVd+4junbvzX8P/C5VWhU6ra5ddu/cRhVfhKymRkWbYrykI/gXc+b1rzq4pHKGPGBDhS58wH1JzyvnybBa/jFFavI94d9y75Obmkp2d3Wz7vy/6iIjB1E38K+7fvkyXix9TGDkEwhY08ddWfYQe8RyBoR7xHHHXrniOsN9zhDmYFVwBLU6/a21qnjllm7u24XH9FzJ//nzeeecdAMaPH0+XLl146KGH2LRpE0899VSLPoE0PdFU/frOpfFInf6Yqc4HQC6XG86Z+iVobLewsBCtVotcLjey29inhnZNNQylUolOpzPpr0KhaJfdhj+bs9v4XhtqaMqu/l5NfddttdvW70avcU1NjVnfTXN2W2ovzWnY8Jrm7vVe7Go0GpPnWrKrL9uS3Xtp30VFRQZ7rd1rY1q7V1dXVzQajVU01Gq1Zv/e3Es7PJ9VRmpOOa4KGZO7e6NUKsxuhw2/7/b2EQEeAczvOR+Q3ko7bR+hroEvHof6CogehW7imyjTrhhsNGfXFHK53OBLVVVVs/dqzT5CJpPx2PAoXt+ZwqZTGUzrGtdh+gh9Wa1Wi0ajobCw0OjNvz36CM2ARRRd+Z6A9K8JOPIK9BgO/ndHMmzZR+gx9znClF2tVkthYSFKpdKgsXiOaGq3vd9Nw2e4wMBA8RzR4Fx727f+Z0ON7fUcYQ5mJbRISEhAo9Fw6tQpo+Opqan07duXDz/8kOXLl5ssGxoaypgxY9i2bZvR8b179zJz5kwOHDjAlClTOHDgAFOnTmXv3r1Mnz7d6Np58+Zx/PhxwzDvwoUL2bJlCzt27GDOnDmG62pra/H09OTXv/41q1evNrLhiAktkpOTDcPljacGCCyD0Ng2CJ1b5tXt59l6JpOHBobx/oJB92RDaNwInQ62PwmpO8E7FJYfBe+Qdpl0BI0r69QM/+tBquo1bH56BAndAlovZCY16hpO5p4kyjuKrp2bzkqxJo6gsRHqOvh0GmT/BCH9YNm34Nr6zBdHxuE07qAIna2PvTW2akKLfv36cenSpSZDnfq5kY3najYuq7+upbL6n81d27AOU+uyGiIyAAoEAkehvFbF7uQ7iSxGRNvZGziSeYQtaVvIq8qztyvt48d/SYGV3AXmrW93YOUoeLm58OCgcODunmiW5q9Jf+WFQy+w4+oOq9h3Klzc4NF/g2cg3L4Ae1+SAneBQCAwE7Oijzlz5lBZWcmXX35pdHz9+vWEhYUxfPjwFsumpaUZZRRUq9Vs3LiR4cOHGxaQhoeHM2zYMDZu3Gg0XzIpKYnLly8zd+5cI5symYz9+/cb1bV//350Oh0jRoww5/bsRlRUFLGxsU0Wuwosh9DYNgidm+ern7OpUWmID/FiSLRf6wWawVIab7q0ib+e/CsH0g+0y45dSf8BvntD+vzLtyCq+b9B5uAo7fixO9kkD6TmUVhZ18rV5jMmYgyhnULp7N659YstjKNobIRvBDyyDmRySN4MZ9bZ26N24ZAad0CEztbH2TRWvPnmm2+29eK4uDhOnDjB2rVr8ff3p7y8nLfeeott27axZs0aw1DdsmXLePjhh1myZIkhO0v//v3ZuXMnGzduJCQkhNu3b/PKK69w4sQJNmzYYJRlJC4ujvfee4/k5GQCAgJISkrimWeeISoqijVr1hjmsQYGBlJYWMhHH31EeXk5CoWCb775hhUrVtCrVy/ee++9JnMudTod9fX1Rsfc3Nzsmsrdw8MDT09PPDw87OZDR0dobBuEzqbR6XS8uv0CRVX1vDChO4Oi7j24spTGJbUl1KprWdJnCX7u9+6P3SjPgX8/CPWV0H8+TPoTWKgfd5R2HOzjzuHLBeSU1tLZU8lQC+95FesTyxO9n2BwyGCL2m0LjqJxE/xiwMUdbhyB64eg2wTwaVvmYUfDYTXuYAidrY+9NTY3djB73tyOHTtYvHgxb7zxBlOnTuXkyZNs3ryZRYsWGa7RaDRoNBqj7Bpubm4kJiYyfvx4XnjhBWbNmkVubi779+9n7NixRnWMGzeOffv2kZuby6xZs3jhhRcYP348iYmJRmkrAd5//33+53/+h927dzN9+nT+8pe/sGDBAg4dOmSUnlEgEAjsxen0Ei7frsBdKWfOAxGtF7ABT/R5gvXT1hPrG9v6xY6Guh62LYGqAgjpCzPft1hg5WgsGi69qd10MgON1rLT1BRyhdgj0hSj/gN6zgStCrY9AZUF9vZIIBA4EWYltOgIOGJCC4FA0LF5ftNZ9p7PZeGwSN6a2/JaUUEb2Ps7OL0W3Hxh+WEI6NZ6GSelVqVhxFuJlFar+PiJIUzqbfk1ZWqtmmul1+jp37P1i+8Xasth7XgougYxY2DxV9LGwwKB4L7DqgktBNZBP9JnKie/wDIIjW2D0LkpeWW1fJMiJY1YPCKm3fbaq7Faq2bPjT2U1ZW12xe7kLxFCqwA5n5klcDKkdqxu1LB/CHSxqnrf0y3uP3S2lLGbh3Lgj0LKK8vt7j95nAkjU3i7gPzPwdlJ0g/BodW2tsjs3F4jTsIQmfr42wai9cwDkBKSopI42llhMa2QejclE0nb6HR6hgW40/vMJ9222uvxj/n/8zvj/0ef3d/Dj96GLnMid6x5V2Ar1dIn3/xCvSYapVqHK0dPz4imo+O3eDY1UKu5VfSPdjLYrY7u3cm0COQ8vpyjmcfZ1rsNIvZbglH09gkwT3hwX9Kqf6Pvw/hg6H3bHt71WacQuMOgNDZ+jibxk70V1UgEAicizq1hk2nMgBYMjLGvs7c4XDmYQBGh492rsCqpgS2Pg7qGug+Cca9Zm+PbEakvycTe0rTATcmWT4t+9hIad2zvm0IGtB3LiT8Rvr81XNQeNW+/ggEAofHif6ydly8vb3x8fHB29vb3q50WITGtkHobMz+C3kUVtYT4uPGlD6WWSvTHo11Oh2HMg4BMCFygkX8sQlaLexYDiXp0DkK5q4FuaLVYveKI7bjJSOlvdG2/5RFZZ26lavNY3zkeAB+yPoBlUZlUdvN4YgaN8ukNyF6FNRXSAF+XaW9PWoTTqWxEyN0tj7OprGYFugAdO3a1d4udHiExrZB6GyMfo3MouHRKBWWeZfVHo2vlFwhuzIbN4UbCWEJFvHHJnz/f3D1WylF9vyN4GnZlOSNccR2PLp7IF2DOnGjoIodZ7N4IiHGYrYHBA0gwD2AotoiTuWdYlT4KIvZbg5H1LhZFEp45FP48BdQkAa7X7izH5ZjZ1p0Ko2dGKGz9XE2jcXIlUAgEFiB81ml/JxRilIhY8GwSHu7A9yd9pUQmoCn0tPO3rSRq9/BkbekzzPehVDHn29vDWQyGUvuBFTrT6RjyUS/cpmc8VHS6FViRqLF7HYovEPg0fUgd4HUHZC0xt4eCQQCB0UEVwKBQGAF/v2jtDZmRr9Qgr3d7eyNhH5KoP5B2uEpvglfPgXoYMivYNCiVot0ZOY+EE4nVwXXC6o4cb3IorYnRU0CpABcq9Na1HaHIWoE/PJ/pM/f/hfcOmFffwQCgUMigiuBQCCwMEWVdexOzgHgCQdJZJFXlcel4kvIkDE2YmzrBeyNqga2LYbaUggfAlPftrdHdsfbXckjg6VNqD87kW5R28O6DMNb6U1hTSHnC85b1HaHYthy6DcPdBr4YilU5NnbI4FA4GCINVcOwM2bN1Gr1bi4uBAbG2tvdzokQmPbIHSW2Homk3q1ln7hvgyK7GxR2/eqsX7UalDwIAI8Aizqk8XR6WDPS1Lqdc9AePTf4OJms+oduR0vTohh/Y+3SLx0m8ziaiL9LTO9U6lQMiZiDPtu7iMxI5GBwQMtYrc5HFnjFpHJYNYquJ0K+Rdh2xJYukdal+VgOK3GTobQ2fo4m8Zi5MoBKC8vp6ysjPJy223geL8hNLYNQmdQa7R8nnQ3/brMwove71Vj/XorfWY4h+bMOkjeBDK5lDjAN9ym1TtyO+4e7MXo7oFodfD5yQyL2p4YNRGQ1l1Zck2XKRxZ41Zx7SQlVnHzgcwk+PaP9vbIJE6tsRMhdLY+zqaxCK4EAoHAghy8lE92aQ1+nkpm9g+1tzsAlNWVcSbvDOAE660yT8P+V6XPk96Erk4whdHG6PdM23I6g5p6jcXsjg4fjavclcyKTK6Wiv2cWiSgG8z5QPp8cg1c2G5ffwQCgcMgpgU6AH369EGn01n8DbfgLkJj2yB0hk9+uAHAwmFRuCstvxfTvWh8KOMQap2aeL94on2iLe6TxagsgG1PgFYFvWbDyN/axQ1Hb8cTegYT6e9BZnENO37OYtFwy3ynnkpPRoaP5EjmERJvJRLvF28Ru6ZwdI3bRM8ZMOY/4djfpPTswb0hpLe9vTLQITR2AoTO1sfZNBYjVw6Ai4sLSqUSFxcR61oLobFtuN91PpdZyun0EpQKmWF0wdLci8YHbh0AYEr0FKv4ZBE0atj+JFTkQGA8PLTabvsIOXo7VshlPDlSWnfwybGbaLWWm8I3OXoy/QP7E+5t3amYjq5xmxn/OnQdB6pqaYPh2jJ7e2Sgw2js4AidrY+zaSyCK4FAILAQa49Jo1azBoQR4uMY6dcB5nafy+ToyUyOmWxvV5rn4J8g/Ri4et1Zz+Jtb48cmkeHRuLt7sKNwioOpeVbzO6srrP4fMbnzO4222I2OzRyBTy8Dnwjofg67HwWtCKVvUBwPyOCK4FAILAAmcXV7L+QC8BTox1rN/kpMVN4d9y7dPV1LL8MXNgOP/5T+vzQagjqYV9/nAAvNxceGx4F3A3qLYGzTLtxKDoFSBktFa5weS8cf9/eHgkEAjsigisHoLS0lOLiYkpLS+3tSodFaGwb7medPz2ejlYHo7sH0jvMx2r1dDiN81Kk9SoAo1+E3g/a1x+cR+OlI2Nwkcs4ebOYC1mWnY5WXl9O4q1Ei9psiLNo3GbCH4Dp/0/6fGglXD9sX3/ogBo7KEJn6+NsGjvH5MUOzq1bt1CpVCiVSjp3tuyeOAIJobFtuF91LqtRsfW0lBb7qTHW3YPDHI3L68vZmraVydGTifGNsapf90RNibRORVUNXcfDBMdIae0s7TjU14NZA8LY+XM2a4/d4O8LB1nEbrWqmklfTKJGXcOeOXuskgTFWTQ2i8FLIOs0/LwBvlwGy49C50i7udMhNXZAhM7Wx9k0FiNXAoFA0E62nMqgql5DfIgXY+OD7O2OgcMZh/n7z3/nxSMv2tuVpmi1sGM5lNwE3yhpPyu55bMrdnSWjZaC+b0XcskurbGITU+lJ4OCB9HNtxuFNYUWsXnfMP3/QehAqC6SMl+q6+ztkUAgsDFi5MoBCAsLQ6PRoFCIBwtrITS2DfejziqNls9OpAPSWitrr1kxR+MgzyBGhY1icMhgq/p0Txx9G65+Cy7usGAjePrb2yMDztSO+4b7ktA1gB9vFPHZ8Zu8PsMyqcDfG/cenkpPi9gyhTNpbBZKd2n91UdjIeestGfbLPusweqwGjsYQmfr42way3TW3obdwdBqtVRUVBgd8/b2Ri4Xg3gCgcB8dp3L5j+2nCPQy43jr43HzcU5On+7krYPtiyUPs/5EAYssK8/Ts6htNv86rMzeLu5cOL3E/B2V9rbJcG1g7DxEUAHD/4LBj1ub48EAsE9Ym7sICIKgUAguEd0Op0hU9uShGgRWLWFwmuw8xnp87DlIrCyAOPig+kW1ImKOjVbT2da1HaNuoYbpZbLRnjf0H2StAcWwJ6XIOecff0RCAQ2QwRXAoFAcI8k3SgmJbscd6Wcx0dYftF/eziQfoC8qjx7u2FMXQVsXQR15RCVAFP+am+POgRyuYynxkhp9j89no5aY5l9ls7knWHs1rG8eORF7rNJLpZhzH9C/FTQ1MG2xVBdbG+PBAKBDRDBlUAgENwj+lGrRwZH4NfJ1c7e3KWopohXv3+VKdunOE6ApdPBruehIA28usC89eDiOJo5O3MGhRPQyZXs0hr2pVjmO+/h3wO1Vs2NshtcLb1qEZv3FXK5NO3VLxZKM2DH06DV2NsrgUBgZURCCwfg/PnzhhST/fv3t7c7HRKhsW24n3S+mFPOobR85DJYZsNNg9ui8YH0A2h0GvoG9KVLpy42861Fjq+Ci7tAroT5G8A7xN4eNYsztmN3pYInEmJ47+AVVh++xqz+oe1OruLt6s3o8NEczjzMNze/Id4v3kLeOqfG94RHZ6m9fzxZWod15G2Y8LpNqr4OENV5AAAgAElEQVRvNLYzQmfr42wai5ErB0Cn0xn+CayD0Ng23E86rzl6HYDp/UKJDexks3rbovHeG3sBmNF1hq3capkr38LBN6XP096GyGF2dac1nLUdLxkZTSdXBWl5FRy+nG8Rm1NjpgLwTfo3FtXDWTW+J7r0g1mrpM/f/6/0ksEG3Fca2xGhs/VxNo3NDq4qKytZsWIFYWFhuLu7M3DgQLZs2dKmsvn5+SxdupTAwEA8PT1JSEggMdH0DvAHDx4kISEBT09PAgMDWbp0Kfn5Lf+xOHjwIDKZDJlMRmGh8+zN4eHhgaenJx4eHvZ2pcMiNLYN94vONwur2Hs+B4DnxnW3ad2taZxRnsH5wvPIZXKmxk61qW8mKbgibaiKDh54AoYss7dHreKs7bizp6th7d8/D12zyIPIuMhxeLh4kFmRSXJBcrvt6XFWje+ZAfNhxHPS552/hrwLVq/yvtPYTgidrY+zaWz2tMC5c+dy+vRp3n77beLj49m0aRMLFy5Eq9Xy2GOPNVuurq6OiRMnUlpayqpVqwgODuZf//oXU6dO5eDBg4wdO9Zw7dGjR5k2bRozZsxg165d5Ofn8+qrrzJx4kTOnDmDm5tbE/uVlZU8/fTThIWFkZOTY+5t2ZX4eMtNtRCYRmhsG+4XnT88eh2tDib0DKZ3mI9N625N4703pVGrhNAEAj0CbeFS89SUwOYFdxNYTP8bWHkfMEvgzO142ehYPj2RztmMUk7eLGZE14B22fNUejI5ejK7r+/m6+tfMzB4oEX8dGaN75nJKyH/Etw4DJsXwtOHwct6m47flxrbAaGz9XE2jc0audq3bx/fffcdq1ev5plnnmH8+PGsXbuWyZMn8/LLL6PRNL9Q85NPPiElJYVt27axaNEiJk+ezPbt24mPj+eVV14xuvbll18mPj6e7du3M3nyZBYtWsS2bdtISUlh3bp1Ju2/9tpr+Pn58atf/cqcWxIIBAKzyC2r4cuzWQA8P76bnb0xRqfTse/GPsABpgRq1PDFk1B8HXwj4dENIoGFDQj2cefRIREA/OvwNYvYnNVtFiBNDazX1FvE5n2JwgXmfQr+3aAsE7Y9AWqhp0DQ0TAruNq5cydeXl7MmzfP6PiTTz5JTk4OJ0+ebLFsjx49SEhIMBxzcXHh8ccf59SpU2RnZwOQnZ3N6dOnWbx4MS4udwfWRo4cSXx8PDt37mxi+9ixY3z00Ud8/PHHTrN7s0AgcE7Wfn8TlUbH8Fh/Bkf729sdI1KLUkkvT8dd4c6EqAn2dea7P0pv6JWesGCTVd/QC4x55hfdUMhlHLtayPms0nbbGxoylBDPEMrry/k+63sLeHgf4+EHC7eAmw9knIB9v5MyaQoEgg6DWdMCU1JS6NWrl1HQAxgyd6SkpDBy5Mhmy44ZM6bJcX3Z1NRUwsPDSUlJMTre+Nrjx48bHaupqWHZsmWsWLGCBx54gN27d5tzS4a6o6Oj8fG5O72nrq6OtLQ0APz8/IiKijIqc/XqVaqrqwEYMGCA0bnCwkJDsBgVFYWfn5/hnEajMdyjt7c3XbsaZxm7efMm5eXlAPTp08dI69LSUm7dugVAWFgYQUHGDyvnz59Hp9Ph4eHRZAg1MzOT4mJpj40ePXrg7u5uOFdZWcn169Li/ODgYEJDQ43KXrx40ZClpXfv3kbncnNzDWvhunXrhpeXl+FcbW0tly9fBsDf35/IyEijsleuXKGmpgaZTNbk+y4oKDBM74yOjqZz586Gc2q1mtTUVAB8fHyIjY01Knvjxg3DTtp9+/Y1CrhLSkrIyMgAIDw8nMBA42lTycnSmgJPT0/i4uKMzmVkZFBSUgJAz549jaanlpeXc/PmTQBCQkLo0sU4Q1tqaipqtRo3Nzd69uxpdC4nJ4eCggIAunfvTqdOd5MjVFdXc/WqlAI5ICCAiIgIo7KXL1+mtrYWhUJB3759jc7l5+eTm5sLQExMDL6+voZz9fX1XLp0CQBfX19iYmKMyl6/fp3KykoA+vXrZ7QLeVFREVlZ0shNREQEAQF3px1ptVouXJDWEnh5edGtm/HITnp6OmVlZQD06tULV9e7IxllZWWkp6cDEBoaSnBwsFHZlJQUNBoN7u7u9OjRw+hcVlYWRUVFAMTFxeHp6Wk4V1VVxbVr0hv8oKAgwsLCjMqmpaVRV1eHi4sLffr0MTqXl5fH7du3AYiNjUWtcGfzKan9LB8dbWgvjtJH7Li0A4CB3gOpLq2mU5Bxog2b9RFnN0DSagBKxr1FRr4O8pNFH2GjPiLS35MHB4Sx4+ds3tl9jldG+bW7j5jRdQbrUtax+/puJkVPEn3EHRr3EW16jgiKh0fWoft8HrKz68lSdyZi7n8b2RXPERKij7iLeI6QsEcfof9b3lbMCq6Kioqa/BKD1OD151sqq7+upbL6n81d27iOP/7xj2g0Gv785z+38S6aolarmyz81el0qFQqw3lTZfTnG6PVag3ntNqmmzk2tpuZmYlGo0GhUBjZbexTQ7umpmCqVCp0Oh1KpbLJOY1G0y67zd1rQ7uN77Whhqbs6u/VVLrgttpt63ej17i+vt6s76Y5uy21l+Y0VKvVRp2LqXu9F7sqlcrkuZbs6su2ZtcULbXvrKwswzlT5Rv61JjW7rW+vh6tVmtydNoSGprSqLHdtcduUKPS0C/cl5Fd/UhNlf5wW7uPaEhFRYXJe1Vr1SRmSwmChvsMt18fkZEEe16UPo99jaroSajy8kzeqyP1EabutaioqMmDk7P0Ec+O68aOn7M5nlHFtR5uxPo1XatsTh8xq+ss1qWs41jWMUpqS+65j2hot6KigszMTKMHZmfvI5qz26S9xE0mf8BvCEn+B+EX/gEDJ0DXcYbT7ekjGrbDjIwMlEqlQWPxHNHUbnv774bPcJGRkU7TRzS060jPEQ3t6n821NhefYQ5mJ3QoqV9M1rbU8Ocss1d2/D4qVOneP/99/nmm2/alUHExcXFZP36zqXxSJ3+mKnOB0AulxvOmfolaGy3uLjY8EbHx8fHcL6xTw3tmmoYSqUSnU5n0l+FQtEuuw1/Nme38b021NCUXb2Gpr7rttpt63ej17gluw3vsTW7LbWX5jRseE1z93ovdvUdjjl29WVbsnsv7Vv/VrOh/eZ8akxr9+rq6opGo7GKhlqtttXfm9IaNetPpAPw24lxRjpYu49oSMM/Kg3v9Xj2cYrrivFWeDPIb5Bd+giP+iLYuhy0Kug1G8a+iuL2bafoIxreqx5TbyudpY+IC/FmRr9Q9l7IZXtaDa+P9TbLbsN7VSgUxPjF0DugNxeLLvJN+jcMUw5rV/vWPygWFxcbBVfO3EeY+xxR3ucJlMVX8M88ANuWwPLD4C+9wG5PH6FvhyqViuLiYqPgSjxHNLXb3v674TNcZGSk0/QRDe060nNEQ7v6nw019vX1tUsfYQ4ynRnhWEJCAhqNhlOnThkdT01NpW/fvnz44YcsX77cZNnQ0FDGjBnDtm3bjI7v3buXmTNncuDAAaZMmcKBAweYOnUqe/fuZfr06UbXzps3j+PHjxuGefv27Uvv3r356KOPDNe8/fbbvPPOO1y/fp2goCC8vY3/oGi1WsNQrx5vb2+TX66tSE5ONjSaxtOHBJZBaGwbOrLOb+9P44Oj1+kb7sPXvxnd7g1a75XmNF5xeAWJGYks7r2YV4a+0oIFK1FXCZ9Og7zzENIPlh0AV9vt/2VJOko7vpxXwdRV36PTwf7/GEOv0PZlttx4cSPvnH6HfoH92DRjU7tsdRSN242qFj6bDtk/QWAPWPattPGwBRAa2wahs/Wxt8bmxg5mjVz169ePzZs3o1arjSJy/dzIxnM1G5fVX9eQxmX1Py9cuNAkuLpw4YJRHampqaSmpvLFF180sdutWzcGDBjAuXPn2np7dqNHjx7odDq7PazdDwiNbUNH1bmoso5//5gOwIqJ8Xa9P1MaF9UUcTTzKABzus+xvVNajbSXVd558AyEhZucNrCCjtOOe3TxZnq/UPaez2XVwat8sHhwu+xNi53GkawjzIid0W59OorG7UbpDvM/h7XjofCylEHw8S9BYfrNvDkIjW2D0Nn6OJvGZo1c7d+/n+nTp7Nlyxbmz59vOD5t2jTOnz9PRkZGs9n61qxZw3PPPUdSUhLDhw8HpLmnAwcOxMvLi6SkJMO1w4cPp7q6mnPnzhnsJSUlkZCQwJo1a/j1r38NwJEjR5rU89lnn7F+/Xq++uorwsPDGTJkiNF5Rxy5EggEjs1b+y/x4dEb9I/wZdfzoxyug9doNZzMO8mZvDP89oHf2t6B/a/CyQ/AxR2W7IHIobb3QWCSq7crmPK+NHq197ej6RPm23ohge3JTYZ100BVBYMWw+x/OMWecALB/YC5sYNZwRXAlClTOHPmDO+88w7du3dn8+bNrF27lo0bN7Jo0SIAli1bxvr167l+/TrR0dJu8XV1dQwePJjy8nLefvttgoODWb16NV9//XWTTYSPHDnC5MmTmTVrFs899xz5+fm89tpr+Pr6NruJsJ4333yTP//5zxQUFDRZiHwvAgkEgvubwso6xrxzmBqVhnVLhzChZ4i9XXIskj6Ab16VPs/7DPrYYeRM0CIvbP6Zr5NzmNI7hI+eGNJ6AYF9uPwNbFkIOi1M/BOMecneHgkEAsyPHcyOKHbs2MHixYt54403mDp1KidPnmTz5s2GwAqkjBsajcYou4abmxuJiYmMHz+eF154gVmzZpGbm8v+/fuNAiuAcePGsW/fPnJzc5k1axYvvPAC48ePJzExscXASiAQCCzN2u+lDIEDInwZ3yO49QL3E5f3w4HfS58nvSkCKwfltxO6I5PBtxdvk5Jd1m57JbUlrE9dz4nsExbwTmCgx1SY+o70OfHPkPKlff0RCAT3hNkjV86OI45cVVZWotVqkcvlRvs7CCyH0Ng2dDSdb5fXMvb/DlOr0vLp0qGM72n/4Kqxxu/+9C5arZbHej1GmFdY6wYsRc7P8Ol0UFXDA0tg1qoOM42po7VjgN9u/pndyTlM6BnMuqXtm7b597N/Z+2FtSSEJvDRlI9aL2CCjqixxfjm99I+cQo3WPI1RA2/JzNCY9sgdLY+9tbYqgktBNbh+vXrItOMlREa24aOpvOqxKvUqrQMifZjXI+g1gvYgIYax/WOY0vaFmrUNYyPGm+74KosCzYtkAKrruNhxt86TGAFHa8dA6yYFMfeC7kcSsvn1M1ihsU23UuyrTwc/zAnck4wJWbKPS8y74gaW4wpf4GSdLi8T5om+NRBQ4p2cxAa2wahs/VxNo3FQiOBQCAwwc3CKraezgTg1Wk9HS6JBYCrwpX//cX/8mj8ozwQ/IBtKq0th88fhco8COoFj663SGYzgXXpGuTF/KHSXkfvfJNm9qaYDQn3CmfLzC08Ev+IQ/5eOD1yBTz8MYQOgOoi6feturj1cgKBwCEQI1cOQHBwcLMbuAksg9DYNnQknf/ft5fRaHVM6BnM0Jh7f8tvaRpq7CJ3YVzkOMZFjrNN5RoVbH8S8lPBKwQWbQP3jpd9riO144b8x/9n78zDo6rOBv67s2/ZN5JAEggQloRNhIK7CEUBF5QWKiou1QL1q9XWahe1da+1rRt1q4IiWFABKwiKdUF2UAIEEsIaErLvy+xzvz9uMsmErJjJJOH8nmeeO3PPct/7zrnnnvcs75kyhI++y2XvqXI2Hy5i6ojAOWfpqzruMnRm+NkqeGMKlGbDf26BWz4CTcfXnQsddw9Cz/6nt+lYrLki8GuuBAJBz+JAbiWzXv4WSYIN//fDN1/tE8gyrF0E6StAY4TbN0B8N42WCbqMZzdm8q+vjjE0xsKnv7oUtercR56qHdWsP76eQSGDmBA7oQulFHgpzIB//xgc1TDierjpLWVkSyAQdBt+9xYoEAgEfZ1nN2YCcP2Y+B5rWD23+zle+v4lSqwl3XPBzY8phpWkVlyuC8OqV/KLy5IJMWo5UljDR9/l/qC83jr4Fk/ufJK3Dr7VRdIJziJmJPz0XVBp4dBaZU+586tPXCDodQjjSiAQCJrwbXYJ3x4tQauWuH/q0ECL0yKl1lJWZq7k9f2vk1+T7/8Lbn8Ftv5T+X7ti4rLaEGvJMSoZdHlyQD84/Mj2Jzuc85r9uDZAGw9s5VTVae6RD5BCyRfAbNfAyTY/QZs+VugJRIIBG0gjCuBQCCox+2ReWL9IQBunpjIgHBTgCVqmY+yP8LpcZIWmUZaVJp/L7Z/NWz6vfJ9yqMwdr5/ryfwO7dNTiI2xMCZShtvbT1xzvkMCB7AJfGXALDi8IquEk/QEqk3wtX1e2D97wnYuyyw8ggEglYRxlUP4NChQ6Snp3Po0KFAi9JnETruHnq7nlftOU1mQTXBBg2/mjIk0OK0yIGMAyw/uByAecPm+fdiR7+AtQuV7xMXwsW/9u/1egi9vRy3h0Gr5sHpKQC88r+jFFXbzjmv+SMUY3vt0bVUO6rbid1IX9exX5h4D1x8v/L9k/sgc0Ob0YWOuwehZ//T23QsjKsegNPp9H4E/kHouHvozXqusjn526YsAO67aihhZl2AJWqZnSU7KXOWEawJZlrSNP9dKG+v4qHM44TUm+DHT/WpvazaojeX445y3eh4Rg8Ipdbh5vlNR845n0mxk0gOSabOVcea7DUdTnc+6NgvTHlEGT2WPYrnzlPbWo0qdNw9CD37n96mY2Fc9QC0Wq33I/APQsfdQ2/W8ytfHqW01sGgKDO3TEoMtDitsrl0MwBToqagV3fcLXOnKDgI784GZy0Muhyu/xecRx5Ve3M57igqlcQjM0cAsGrvaQ7mVZ5TPpIkcfOImwFYkbkCt6dja7jOBx37BUmCmS/A0KvBZVP2wMr7rsWoQsfdg9Cz/+ltOhau2BGu2AWC851TpbVM/fs3ONwe3lowniuHBW7/n7Y4Un6EGz++EbWkZuONG+ln7tf1Fyk5Cm9Ph9pi6D8BblkDekvXX0fQI/i/ld/zcfoZJg4M5/27f3ROmwJbXVamfjCVSnsl/7zin0xJmOIHSQU+OK3w3hw4uQWMYbBgveJZUCAQdDnCFbtAIBB0kqc3ZOJwe7hkSCRXpEQHWpxWWXpwKQBTEqb4x7AqPwXvXKsYVv3S4ObVwrDq4/zu6mHoNSp2nihjU0bBOeVh1Bi5achNACw/tLwrxRO0htYI81ZC/HiwlsM71ysdIwKBIOAI40ogEJzXfHOkmI0ZBagk+NPMEefUc98d5Nfk8+mJTwG4I/WOrr9AVb5iWFXlQWQK3LIWjKFdfx1BjyI+1Mjdlw4C4PFPDlPncJ1TPnOHzUUtqdlTuIfMssyuFFHQGvogmP+B0hFSW6Q8v+XCJb5AEGiEcSUQCM5bbE43j6w7CMCCyQMZGhMUYIla551D7+CSXUyMncjIyC6e/lNbAu9cB+UnISwJbl0H5siuvYagx7Lw8mTiQ43kVVh5+X/nNvrRz9yPqYlTAViasbQLpRO0iTFM6QiJTFE6Rt65TukoEQgEAUMYVz2A/Px8cnNzyc8XFaK/EDruHnqbnl/9+hgnS+uICdbz66k90/U6QIWtgg+zPwTg+rjru1bHtaX1U4qyIDgebv0YgmO7Ju9eSm8rxz8Uk07Do7MU5xZvbDnO0aKOu1RvyoLUBQB8euJTTledbjPu+aZjv2KOhFvXKh0j5SeUEazqAqHjbkLo2f/0Nh0L46oHUFRUREFBAUVFRYEWpc8idNw99CY9nyypZclXxwBlOmCQoed6IVqZuRKry8rw8OH0d/XvOh3XlsCyWVB4AMzRimEV1nM9JXYXvakcdxXTRvbjquHRON0yf1x7kHPxdTUyYiQXx19MqD6UU9VtT087H3XsV4Lj6jtG+kPJEVg6g7JTh4SOuwFRlv1Pb9OxMK4EAsF5hyzLPPJxBg6X4sRiRlrPHqlJCE4gISiBO1Lv6Lo1YTXFimFVlAGWfnD7Bogc3DV5C3olj84aiUGrYsfxMtbuyzu3PCY9ysYbN3Jx/MVdLJ2gXcISYcEnEDIASo8yeMv/obUWB1oqgeC8Q7hiJ/Cu2GtqavB4PKhUKiwW4ZnLHwgddw+9Rc/r9+ezeMV36DQqNt13KQMjzYEWqV0a9g+y1ll/uI5rihTDqjgTgmLhtk+EYdWE3lKO/cErXx7luU1ZRFp0fHH/5YSY/DOiez7r2O+Un4Sls6AyB3doErafrsYcOzTQUvVZRFn2P4HWcWdtB2FcEXjjSiAQdB9ltQ6m/eNrSmoc/GrKEH499TxrdFQXKIZVyREIilN6uiOSAy2VoIfgcHm45sUtHC2q4cZx/Xn+J6PPKR+P7OHLnC8ZHT2aSKNwjtLtlJ+CZTOhIkdZi3XbJxA6INBSCQS9ErHPlUAgELTBn/+bQUmNg6ExFhZd0bONio+PfcyqrFU43c6uybAyD5bOVAyr4HhhWAnOQqdR8eyNaUgSfPhdLl9mndsahz98+wfu++o+3j30bhdLKOgQYYmwYAOEJtaPZM2AshOBlkogOC8QxpVAIDhv+PxQIev2nUElwXM3jUavUQdapFapc9bx/J7neXzH42w4seGHZ1hyFN76MZRmK2syFqwXhpWgRS5IDOeOiwYC8PCHB6iydd64n5Y4DYvWQpCu525v0OcJHaCspQwbCBWn4K3pUHgo0FIJBH0eMS2QwE8LtNlsyLKMJEkYDIaAydGXETruHnqynivrnEz9x9cUVdu557JBPHz18ECL1CYOt4PVR1az8cRG3pr+FlqVsvblnHScvx+Wz4baYogYrOyLI6YItUpPLsfdhdXh5uoXvuFkaR1zLxzAMzeO6lR6WZapcda0alwJHfsfr45rCjGsngdFh8AQCvM/hP7jAy1en0GUZf8TaB2LNVft0BONq/T0dJxOJ1qtltGjz21+u6BthI67h56s5wdWpfPhd7kMijKz4f8uwaDtuaNWTWl4oTTQaR2f2gYrfgr2Kug3CuZ/BJYoP0rc++nJ5bg72Xm8lJ++vgOAd++cwCVDuq7cCB37Hx8dDxkAK34CubtBa4a570HyFYEWsU8gyrL/CbSOxZorgUAgaMZnGQV8+F0uUv10wN5iWAE/zPX6kc/g3RsUwyrxImWNlTCsBB1k4qAIFkxOAuDBD/ZTWXdua/+2ndnGG/vf6ELJBJ3GFK6MWA+6Apy1iqF16ONASyUQ9EnUjz322GOBFqI7kWUZh8Phc06v13fd3jHngNPpxGg0YjabCQkJCZgcfRmh4+6hJ+q5oNLGbW/vwub0cM+lg/jJhT17OlyFrYI7Nt2BWWtmUOigs+qmDus4/X348A5wO2DodJi3EvTCTXBH6InlOFBMGBjOhgMFnC63klNWyzVpsZ16Xx6rOMb8DfPZXbibqxKuIsIYAQgddwdn6Vijg5E3KA5tig7BoXVgiYG4sYEWtVcjyrL/CbSOO2s7dHrkqqamhvvuu4+4uDgMBgNjxozh/fff71DaoqIiFixYQGRkJCaTiUmTJvHFF1+0GHfz5s1MmjQJk8lEZGQkCxYsOGtn5r1797J48WLS0tIICgoiJiaGq666iv/973+dva2AMmDAAJKSkhgwoGc3+nozQsfdQ0/Ts8cj88DqfVTUOUmND+aBaSmBFqldXt3/KgdKDvDmgTdbDG9Xx7IMXz0La+4BjwvSfgI/XQ5aox+l7lv0tHIcSEw6DS/MHYNGJbHhQAGr9+R2Kn1yaDJTE6fikT28+N2L3vNCx/6nRR1r9HDT2zDuVpA98Ml98Pmj4PEETtBejijL/qe36bjTxtXs2bNZtmwZjz76KJ9++ikXXngh8+bNY8WKFW2ms9vtTJkyhS+++IIXXniBdevWERMTw/Tp0/n666994n799ddcffXVxMTEsG7dOl544QU2b97MlClTsNvt3ngrV65k165d3HHHHaxbt44333wTvV7PlClTeOeddzp7awKBoI/xxpbjbD1ailGr5oW5Y9FpevZM6GMVx3g/U+msemD8A6ikTsrrcsDaRfDVU8rvi+6DG14DtX82ghWcH4zqH+rtmHj04wyOF9d0Kv29Y+9FLan5Kvcrviv8zh8iCjqDSg2zXoTLH1Z+b/2nMsrttAVWLoGgj9AphxYbNmxgxowZrFixgnnz5nnPT5s2jYyMDHJyclCrW17LsGTJEhYvXsy2bduYNGkSAC6Xi9GjR2OxWNi5c6c37oQJE6itrSU9PR2NRgPAtm3buOiii1iyZAkLFy4ElJGw6Ohon+u43W7GjRtHbW0tR48ePUuOnujQQiAQdD0HciuZ/a+tON0yz8xOY+6EhECL1CayLHPP5/ewPX87Vwy4ghevfLH9RE2xVsB/5sPJLSCpYcbzMP52/wgrOO/weGRufnMn24+XkhYfwocLJ3eqs+LP2//MB0c+IDUilfdmvNf5jgOBf9i3Ej6+FzxOGDAR5q4Ec0SgpRIIehR+dWixZs0aLBYLc+bM8Tl/++23c+bMGR8DqaW0KSkpXsMKQKPRMH/+fHbt2kVeXh4AeXl57N69m1tuucVrWAFMnjyZoUOHsmbNGu+55oYVgFqt5oILLuD06dOduTWBQNCHqLQ6+eXK73C6Za5O7cdPe/g6K4Cvc79me/52tCotvxn/m84lLj8F/56mGFY6C/xslTCsBF2KSiXx95+OJtSk5UBeJU9tONyp9IvHLMaitXCw9CAfZX/kJykFnWbMPLhlDRhC4PROeHOKsieeQCA4ZzTtR2nk4MGDDB8+3MfoARg1apQ3fPLkya2mveSSS84635A2IyOD+Ph4Dh486HO+edytW7e2KaPL5WLLli2MHDmy/RuqJyMjg8TERIKDg73n7HY7mZmZAISFhZGQ4NvrnZ2dTV1dHcBZbiFLSkq8xmJCQgJhYWHeMLfb7b3HoKAgBg0axJEjR3C5XGg0GrRaLVVVVQCMHDnSR9cVFRWcOnUKgLi4OB5Z+mQAACAASURBVKKifL1+7d+/H1mWMRqNDB061Cfs9OnTlJWVAZCSkuKzT0BNTQ3Hjh0DFIM1NjbWJ+2hQ4e8LjBHjBjhE5afn+9dC5ecnIzF0rhg3mazkZWVBUB4ePhZc2WPHDmC1WpFkqSz/u/i4mLOnDkDQGJiIqGhod4wl8tFRkYGAMHBwQwcONAn7fHjx709DKmpqajVaq+OZVnG5XIBEB8fT2RkpE/a9PR0AEwmE0OGDPEJy8nJoby8HIBhw4ah1+u9YVVVVZw4cQKAmJgY+vXr55M2IyMDl8uFXq9n2LBhPmFnzpyhuLgYgMGDB2M2m71hdXV1ZGdnAxAREUH//v190mZlZWGz2VCr1aSmpvqEFRUVkZ+fD0BSUpLPIlCHw8Hhw0rjKCQkhKSkJJ+0x44do6ZGmfqTlpbm0ztTWlpKbq6y7qJ///5ERDT2cmZlZXnThYaGkpzsu0ntyZMnqaysBGD48OHodDpvWGVlJSdPngQgNjb2rM6TgwcP4na7MRgMpKT4rp3Kzc2ltLQUgOTBg3ngg0OcKq2jf5iRP05PZv/+/QBERUURFxfnkzYzMxO73Y5Gozmr3igoKKCwsBCAgQMH+q2OMAebeW73cwDMHz6f8hPllFPurSOakp6e7i3Do0ePRnN6O6y+DepK8Vj6kT3hKWx1UcQVF4s6go7XEQ2Ul5dz/PhxQFmw3Py5Op/riNgQI8/dNJqfv7OHpdtOEiFXcWmSqUN1RKQxksVjFvPs7md5ftfzRJVHEawLxmw2+5TF7qgjhgwZgslk8oY1nenSU+uI9toRTTlx4gRVVVW4XC4MBgNardar4xbbEQMvgTs/h/dugvITuF67jIKLnqL/5bf55CvqCIXy8nJycnIApR1RVlbmbcMNHTr0vK4jmnKu7QiPx8OBAwcAsFgsJCcn+7STdTpdt9cRDc9pR+mUcVVaWnrWQwxKgW8IbyttQ7y20jYcW4vb1jUAHnvsMY4ePcratWvbjNeUhkZ3U2RZxul0esNbStMQ3hyPx+MN87SwSLR5vlar1VvpSJLkDW8uU9N83W53i/nKsoxWe/b6Crfb/YPybe1em+bb/F6b6rClfBt02JK3lY7m29H/pkHHarXaK0tH/pvW8m2rvLSmQ5fL1eIQclv/TUfydTqdLYa1lW9D2vbybYm2yrfVavVeq6X0TWVqTnv36nA48Hg8LU49bprv61tOsflwETqNilfnX0CIQU1+B+61JR119L/5oXXEe4ffI6c6h0hjJHel3sWRg0fazFeWZZBlpF2vwed/AtkN/UZRec1rVBfVQStlQtQRvvm2hMfj8d5/c+9QIOqIqSNiWHxFMq98eYyXd5URb5FIa5autTpi7rC5fJT9EdkV2awuXM2CuAVYrdZWZWpOV9UR56rDQNYRLcnUkXytVqtPnFaf5agUuOsLav59HZbyQ8R/fR9oypR1m/XPn6gj8ObVNN+mbbiGe+1Ivn21jmieb0t0tHw3LccNOlar1QGpIzpDp4wraHvPlfbcs3YmbWtx28rjzTff5Mknn+SBBx7guuuua1OWpmg0mhav3/CgNB+pazjXUgMFQKVSecNaegia5ytJkvfTNN/mMjXNt6WCodVqkWW5RXnVavUPyrfpsbV8m99rUx22lG/Dvbb0n3Y0347+N0113Jn/prV82yovremwaZzW7vVc8nW73S2GtZVvQ9q28j2X8t30Ou3da3Pau1edTofb7W4z3+/zbbz0ldLz98T1qaTGh1BbW9vuvXo8nk4/N11VRxTZing1/VUAfjXuV5i15jbzlSQJXDYSD/wDde7nyslRP4VZLyDV2tGWn2rzXkUd0f5/0zSf5og6Au6fmsL2I/l8l1fH33ZUcuUkJ6Gmxh741uoIjUrD7yf8nts/u51vyr/hktBLGB46vFWZmtMVdURL99oRHQayjjjXd1VDQ7GpXG0+y5ZoTlz6EnH7/kHEqU9g82OQnw7XvQI6s6gj6mn+3zRtXzS9x/O5jmgI+6Hlu+m1Gz6BqiM6Q6ccWkyaNAm3282uXbt8zmdkZJCamsprr73G3Xff3WLa2NhYLrnkElatWuVzfv369cycOZNNmzYxbdo0Nm3axPTp01m/fj3XXHONT9w5c+awdetW7zBvU95++23uuusu7rrrLl599dVWFSEcWggEfZPTZXXMevlbKuqczJuQwNOzm/en9zxkWWbh5oVsPbOVsdFjWTp9afsL/Stz4f2bIX+f4rhi2uPwo0Xe3mWBoDsoq3Uw66VvyauwctXwGF6/5QJUqo6VwT98+wc+PvYxIyJGsOKaFahVvWdT7/MCWYY9b8GnDyrbOUSPhLnvQfjA9tMKBH0Qvzq0SEtL4/Dhw2cNdTbMjWw+V7N52oZ4baVtOLYWt6VrNBhWt912W5uGlUAg6JtUWp3cvnQ3FXVORvcP4bFrR7SfqAfw8bGP2XpmKzqVjj9P/nP7htXRL+C1yxTDyhiuLESftFgYVoJuJ9ys41/zx6HTqNh8uJBnN2Z2OO2vL/g1Fq2FQ6WHWH54uR+lFJwTkgQX3gm3fQLmaCjKgNcvh6xPAy2ZQNAr6JRxdcMNN1BTU8OHH37oc37ZsmXExcUxceLENtNmZmb6eBR0uVwsX76ciRMneheQxsfHM2HCBJYvX+4zX3LHjh1kZWUxe/Zsn3yXLl3KXXfdxfz583nzzTeFYSUQnGc43R4WvbeXo0U1xIYYeP3W8eg1Pb8nvMRawl93/xWARWMWMTCkjV5ht1OZorN8NtSVQL80uPsrGHRZd4gqELTIqP6hPHeT4kTgtW+Os2JnTofSRRojeWD8AwC8dfAt6pydWywu6CYSJ8E9X0P8eLBVwMq5sPFhcNnbTysQnMd0alogKHta7dmzh2effZbBgwezcuVK3njjDZYvX87NN98MwJ133smyZcs4duwYiYmJgOI154ILLqCqqopnnnmG6OholixZwn//+182b97MZZc1NhK++uorpk6dyqxZs1i0aBFFRUU89NBDhISEsGfPHq93ldWrVzN37lzGjBnDSy+9dNbw3NixY308sYCYFigQ9CVkWeahDw/wnz2nMevUrP7FZEbEBbefsAew/cx27v/qfhKCE3jvmvfQqFpZAluRAx/cCbn107HH3wk/fhK0xu4TViBogxc2Z/OPzUdQqyTeXnAhlw6NajeNLMu8vO9lbhxyI3GWuHbjCwKIy6F07ux4RfkdOwbmvA3hZzs4Ewj6Ip21HTptXNXU1PCHP/yBVatWUVZWxrBhw3j44YeZO3euN86CBQtYtmwZJ06c8HHNWFhYyIMPPsgnn3xCXV0dY8aM4fHHH+eqq6466zqff/45jzzyCPv27cNkMjFz5kyee+45H7eKDddpjebXh55pXBUXF3sXEzZ3nSzoGoSOu4fu1vMrXx7luU1ZqCT4920XcsWws/e+68kU1BZgdVlbH7U6/F9YtxhslaAPhmtfojj6IlGW/YyoLzqHLMs8sCqdj77PI0ivYfXCSQzr13Ynh9Cx/+lyHWd9CmsXgrUcdEEw65+QdtMPz7eXI8qy/wm0jv1uXPV2eqJxlZ6e7nUx2XyvC0HXIHTcPXSnnlfszOH3a5S1mX+5biS3Tkry6/W6FXs1fPZH2LtU+R1/Adz0FoQlibLcDQgddx67y80t/97FrhNlRAXpWX3PJJIiza3Gb67jbXnbiDBGkBKe0moaQefwSzmuzIUP74Kc7crv0T+D6U+DMbTtdH0YUV/4n0Dr2K8OLQQCgaAnsG5fHn9YqxhWCy9P7jWGldPtZNHmRXyb923rkU5sgX9NbjSsJt8Lt2+EsKTuEFEgOCf0GjVv3DKeYf2CKK62c/ObO8mvtLafEPgo+yPu2XwPD37zoFh/1dMJ6a84urj0t4AE6SuU+uro5kBLJhD0GMTIFYEfuaqoqMDj8aBSqXx2EBd0HULH3UN36PnzQ4X8Yvle3B6ZW36UyF+uG9lrHNksPbiU5/c+T4g+hI2zN2LRWRoDHXXKuoZdrym/QxOU/WUGXuqThyjL/kfo+Nwpqrbx09d2cKKklkFRZlbdM4lIi/6seE117DF4mPPxHKYlTeP+8fejVbW8h42gc/i9HOfshLW/gLLjyu8LFsC0J0Af1PXX6sGI+sL/BFrHYlpgO/RE40ogEHSMb44Uc9c7e3C4PMweG8/f5ozu8N46PQG7287fdv+NSXGTuDLhysaAnB2wdhGUHVN+n6eNFEHfIK/Cypx/beNMpY3hscG8d9dEws26NtNU2isJ0Yd0k4SCLsNRB1/8GXYqG6G31ikkEPRmhHHVDsK4Egh6J59lFPDLFd/jcHuYNiKGJTePQ6Pu5c9tXZkyWvVdvWOeoDi47iUYfLaTH4GgN3G8uIafvLaDkho7Q2MsLL9zItHBhg6ldXqcFNQUMCB4gJ+lFHQZJ75RnO9U1LvjHz0Ppj4OFuHgQdD7EWuuBAJBn+Pj9DMsfO87HG4P16T14+Wf9R7DqtJeyRv738Dtady3D1mGfSvg5fGNhtXY+bBouzCsBH2CQVEW3r/7R8QE6zlSWMNPX9/BmYr212CVWku5a9NdLNi0gBJrSTdIKugSBl4KC7cpW0UgQfpKpX7b8zZ4PIGWTiDoVnpH66SP43K5cDqduFyuQIvSZxE67h78oedVu0/zq/e/x+2RmT02nhfnjkWn6R1Vl9Pj5IGvHuDF71/k8R2PKyeLMmHpDMWlcV0pRA1XHFZc90qHPG6Jsux/hI67hsHRFlbdM4n4UCMnSmqZ8+p2TpbUAq3r2KAxUG4vp6iuiF9+8Uvh4OIH0O3lWB8EM/8Od21WNjq3VcAn98Fb06DgQPfIEABEfeF/epuOxbRAAj8tMNAuJs8HhI67h67UsyzLvPBFNv/cnA3AvAkJPHl9aq9ZYyXLMn/e/mc+zP4Qk8bEO5e/SMr+j2D3m+BxgdYEl/0OJi0GdccX8Iuy7H+EjruWMxVWbn5zJydKaokw63j91vFoKnJa1XFOVQ7zN8yn3F7OxfEX8+KVLwonF+dAQMux2wW734D/PQGOGpBUMO42uOL3YOld+xG2h6gv/E+gdSymBQoEgl6P3eXmgVXpXsPqnssG8dQNvcewAvj3wX/zYfaHqCQVf426mJR35iiLvj0uSLkGFu+Ei+/rlGElEPRG4kKN/OeeH5EaH0xprYN5b+xga07rI1IJwQm8POVlDGoD3+Z9y+PbH+c86wfu/ag18KOF8MvdMOJ6kD2w9214cSx885ziCEMg6KOoH3vssccCLUR3IssyDofD55xerw+oK2er1YpOp8NoNBIWFhYwOfoyQsfdQ1fouaLOwZ1L97D5cBFqlcST16ex6PLBvcbdOsC7h97l73v/DsCDdTLXZn4JbjvEpMGNb8ClvwHDuXlGE2XZ/wgddz1mvYbrxsRzpLCa7KIatp62EmQyMj4prEUdx5hjSAlLYePJjRwuO4xH9jAhdkIAJO+99IhyrA+CkTdA0qVQdEhxeHHiG0h/H4zhED0SelHd3hI9Qs99nEDruLO2g5gWSOCnBQoEAoUDuZUsfG8vueVWLHoNr9w8jsuG9i5vUysPr+SpXU8BsLC8kkUVlRAUC1f+CUbPBZU6wBIKBIHD7ZF5/JNDLN12EoAZo2J59sZRWPSaFuOvPrKav2z/CwC/GP0LFo1e1Ks6WgRN8Hjg4IeK6/bK08q56BHK9Ojh14Johwl6KJ21HcTIFYEfuRIIzndkWWblrtMsWvEd5XVOBoQbeffOiYxPCg+0aB1Hlvlgy2M8kfE6AHdWVPLLWhfSpb+Fm/4N/S9Q1h0IBOcxKkni8pRows06tmSXkFVQzcaMAiYlRxDRwmbDIyNGYtQY2Z6/nT2Fe3C4HUyMnSje2b0RSYKYkTD+dtBbIO87qMqFQ2vh8CdgjoSIob1+JEvQ9xAjV+0gRq4Egp5Fjd3FI+sO8tF3eQBcNTyG5+eMJsTUS9YieTzIWRt4Z+tf+JtWcTV9a7WV36TcjDT5/8AcEWABBYKeyd5T5Sx+7zsKqmwYtWqeuD6V2ePiW2ywLD+0nGd3PwvALSNu4bfjfysMrN6OtRx2/Ev52KuUczGpcOlvYfgsMcov6DGITYTbQRhXAkHPYefxUh5YnU5uuRWVBL/98TDuuXRQ73Bc4aiD9JW4d7zC3+RSlocEAzDfPJgHp7+BZIkMsIACQc+ntMbOr97fx7dHlT2tpo/sx5M3pLY4ivWfzP/wxM4nALg2+VoenfQoOrWuW+UV+IG6skYjy1HfPgtLgh8tgjE3K6NcAkEAEcZVO/RE4+r48eO4XC40Gg2DBg0KmBx9GaHj7qGjerY53Tz/WRZvfnsCWYb+YUaenzOaiYN6wShPTRHsekNxqW4t488RYXwQHATAb0Yt5NYxC/3aoy7Ksv8ROvY/TXWcmDSQf311lH9uzsblkYm06Hh69iimjog5K92a7DX8efufiTRG8v7M94k0ik6M1uh15biuTPGouut1ZVQLFMc/4++ACXdDcFxg5WuFXqfnXkigddxZ26HlFaSCbqW6utrrv1/gH4SOu4eO6PmbI8U8+nEGJ+o3E5174QD+OHNEqwvaewSyDCe/hb1L4fDH4K6fex2ayA2ps9mU/xl/mvQnrh54td9FEWXZ/wgd+5+mOlarJH555RAuT4nmgVXpZBVW8/N39jAjLZY/zhxObIjRm+6GITcQbYom3BAuDKt26HXl2BSu7IN10X2QvgK2L4GyY/DtP2DbSzBsBlywAAZe3qOcX/Q6PfdCepuOe3BrRiAQ9CXyK608/skhNhwoACA6SM/Ts9OYMvzs3ukeQ20J7FuhGFVlx7ynC/qPo9+kX8HwWYxSqdnkeIAgXVDg5BQI+gCp8SGs++VF/OPzI7yx5TjrD+TzZVYR9101hNsvGohWrTSoL4q/yCfdmuw1qCQV1yZfK9Zh9QV0JrjwLrjgDjjyKWx7GXK2waF1yicsSdmQeMzNENSD3x+C8xYxLZDATwt0u93e72q1WMDpD4SOu4eW9Fxtc/LGlhO8ueU4dQ43apXEgslJ3HfVEIIMPbAXymmD7E1wYDUc2dQ4SqWz4Em9ib8F6ViV9yXLr1nOsPBh3S6eKMv+R+jY/7Sn40NnqvjTuoPsPaVMD0uOMvPg9GFMGxHjY0DlVOUw++PZ2N12Xr7yZS4bcJn/he8l9KlyXHAQvlsG6f8Be6VyTqWBIdMg7SYYerVilAWAPqXnHkqgdSzWXLVDTzSuBIK+iN3lZsXOHF7631HKahUDZXxiGI9fn8rw2OAAS9cMjxtOboH9q5Vpfw2eqwDixsIFt0PqjaC3cP9X9/P5qc+5/4L7uT319sDJLBD0cTwemQ/25vLMxkxvHTIuIZTfTR/mXZ/p9rh56+BbpBen8+KVL6IS2x30bRx1kLFGmU2Qu6vxvM6ieBhMu0mZNqgWE7MEXYcwrtpBGFcCgX+ptbt4f/dp3txynPxKGwCDIs389scpTE/t13Om7ThtcOJryPwEsjZCbVFjWHB/SLsR0n5CTXgSbtlNiD4EgOK6Yg6WHOSKhCsCJLhAcH5RZXPy+tfH+fe3J7A6lR7sSYMiWHh5MpcMiUSSJDyyx2tYVTuq+fvev/OLUb8gxiymjfVZijLhwCpllkFFTuN5U4QykjVsBgy6PGAjWoK+gzCu2kEYVwKBfyiqtvHejhyWbT9JRZ0TgJhgPfddNZQ5F/RHo+4Bz1hNERz7H2Suh6NfgLO2McwQCiOvh7SfQMIknLhZk72GJfuWMCF2An+99K+Bk1sgEFBUZePF/2Xz/q7TuDxK0yU1Ppi7L01m+sh+6DRKHfP0zqdZkbkCk8bEojGLmDtsLnr12a7dBX0EWYbTuxRDK2MN1JU2hmmMMHgKpFyjHIP6BU5OQa9FGFft0BONq/LycjweDyqVirCwsIDJ0ZcROvYPsiyz80QZ7+44xaaDBd4Gz4AwA4uuGMLscfHoNQGcg+60wekdikF17H9QcMA3PChO6d0cdg0kXgwaHR7Zw+ZTm3nx+xc5VXUKgISgBFbMWOEdvQokoiz7H6Fj//NDdHymwsobW47z/q7T3pGsSIueeRMGMG9CAhXuEzy540n2l+wHIMYUw92j7uaGwTegVffAdZ5+4rwsx24n5GxXOtAyN0Bljm949EhIvgKSr4TEyaA1tpxPJzgv9dzNBFrHwrhqh55oXKWnp3tdTI4ePTpgcvRlhI67lpzSOtbuy2PtvjyOFzeO/qRE6Jgx2MjFSRbGjR3T/YI5aiF3N+TsgFPblN5Ml9U3Tr80GDpdMapix0D9NEWH28H64+tZlrGMY5WKZ8BwQzj3jLqHOUPn9JhGmSjL/kfo2P90hY7Lah0s23aSFbtyKK62A6CS4OIhUVw3ph8Ow07ezHiVojplym+8JZ7bR97OrORZmLR9f6rYeV+OZVnpUMvaAFmfQn460KTJq9bDgAmQMAkSJ0H/Cee0YfF5r+duINA6FvtcCQQCv3CypJbPDxXy6cF8vsup8J436dRcNyae+T9KwFV8EqfTiVrVDeuqPB7FPfqZ7+HMPmWEKj8dPC7feJZ+Si9l8pXK/HtLlE9wfk0+646t4z9Z/6HEWgKAWWtm/vD5LBi5AIuu8y9bgUDgf8LNOn49dSi/vHIwn2UU8u6Ok+w4XsY3R4r55kgxRm0QVwx/ignxe9lWuoq8mjye2PkEL3z3AtcPuZ55KfMYEDwg0Lch8BeSBLGjlM/lD0FtKZz4qn4mw5dQlac4Mjq5pT6+Wul8S/iR4sgobixEDAaV8AAo6Bxi5IrAj1yVlJR4hzsjI8WmiP5A6LjzWB1u9p4qZ+uxEr44XMiRwhpvmEqCiwZHct2YeH48MsbrUt1vena7oPyEYjw1GFP56eCoPjtucHxjT2TCZIge7h2daqDOWceXp79k7dG17MzfiVzfmxltiuaW4bdw49Abe+y+VaIs+x+hY//jLx2fKKll3b481n6fx8nSOu95rcZJcvIhavVfUeHM954fFz2OGYNmcNPQm/qcp0FRjttAlqEkG05tVaYRntp+9hRCAK0ZYkdD3BjF2IodDeGDoMlMBqFn/xNoHYtpge3QE40rgaAnYHW42Z9bwfbjpWw7Vsq+nAocbo83XK2SmDgwnKkjYpiRFkt0sKHrhXA7ofQYFGdCcVbjsTS7cb+ppmiMSk9j3FiIv0AxqEIT2r3MX7b/hdVHVnt/X9jvQm4YfAPTk6b3mOl/AoHg3JFlmfTcSj49mM/nGYUcL2mYvuxBbc7GHLUd2ZgFyAwKHsqa6z5AVT/iXmItIdIoGsnnHZW5ypTy3D1KJ17BfnDWnR1PpVVGtKJSlM67qBSIGgbhyaDRdb/cAr/jd+OqpqaGP/7xj6xatYqysjKGDRvGQw89xNy5c9tNW1RUxIMPPsgnn3xCXV0do0eP5oknnmDKlClnxd28eTN/+tOfSE9Px2QyMXPmTP76178SHR3tE8/pdPLUU0/x9ttvk5+fz8CBA1m8eDH33ntvizII40ogAJvTTVZBNftzK9ifW8mBvEqOFFbjaVYb9As2MDk5gkuGRnJFSjShph/44pBlsFVCxSkoOwHlJ5URqfKTyqfiNMjultNqjBAzsn66Rn0vYmRKu/uZvJr+Kp+d+oyHJzzMhf0uBOCb3G94eufTzEyeybXJ1zIgSEwNEgj6MkeLath8uJCtR0vYc7Icq9ONpKlEE5yO7ArGYB9Panwww+J0rCm9k3jLAFbP+g9m4cb7/MXjhpIjykyJM98rn8IMXy+zTZFUENIfwgZCWJLyCW/y3RB61iwKQe/A78bVtGnT2L17N8888wxDhw5lxYoVvPnmm7z33nv87Gc/azWd3W5n/PjxVFRU8MwzzxAdHc0rr7zC+vXr2bx5M5dd1rir+tdff81VV13FjBkzWLx4MUVFRfzud78jLCyMPXv2oNc3ulT9+c9/zrvvvsvjjz/OhRdeyKZNm3j22Wd54okn+P3vf/+DFSQQ9FZcbg+F1Xbyyq0cL67haFENR4trOFZcQ265lZae/KggPRMHhjMpOYLJyZEkRZg6vi+V0wq1JVBdANVnoCq/ybH+U5Xf+oupAZ2lsSew6TEkAVp4TmVZpqiuiKzyLA6VHiK7PJu/XvpX1PXz5H/3ze/YcGID94y6h1+O/SUAHtmDhNRz9twSCATdhsPlIT23gm1HS9l2rIT03ApsTmWUXm06hjHh38iOcFw5DzIoysLgaAs56tfQaV0MjxjGuH4jGRszggHBA/rcVEJBO3g8UJXbZGZFprLfVnFWy9PUm6I1QVCs8gluOMb5njNFin25eiB+Na42bNjAjBkzWLFiBfPmzfOenzZtGhkZGeTk5KBWt7zwb8mSJSxevJht27YxadIkAFwuF6NHj8ZisbBz505v3AkTJlBbW0t6ejoajdIrvW3bNi666CKWLFnCwoULAcjIyCAtLY0nn3yShx9+2Jv+7rvvZvny5eTm5hIeHv6DFCQQ9DQ8HpkKq5OyWjulNQ7Kah2U1DrIr7CSV2HlTIWVMxU2CqpsuJsPRTUh3KwjLT6EUf1DSIsPYfSAUGLMGrBX1X+qwVZ/tFcpI07WCqgrUfYR8X7KlGNL0ydawxzd2JvXtIcvNFF52TQxemRZpspRRWFdIUV1RRTWFpJTncPp6tOcqjrF6erTWJt5BFx33ToGhQ4C4Pui7ymqK2JCvwmEGYSbXIFA4IvL7eFocY0yip9byfe5Z8guO4W9Lq4+hoxl6GNIartPOknWYSCaUG0/IgyxxJrjSQpOIDE0luSwOAZFRGHSiWnG5wWyrHQsNszC8H7qZ2bUFHY8L41R2QjZFF5/jABzpHI0hoEhBPRBoA9Wjobgxu9iWrtf8Ktx9fOf/5z333+f8vJyr9EDsHLlSn72s5+xdetWJk+e3GLaqVOncvr0aTIzM33OP/300/z+978nNzeX+Ph48vLy6N+/P08//TQPdY5lAwAAHB9JREFUPfSQT9yUlBQSExP57LPPAHjyySf54x//SH5+Pv36NW4Mt337diZPntziaFpPNK4C7WLyfCBQOnZ7ZGxON3aXB7vLjd3pwVZ/bDhncyrHWruLaquTOpsNq9WKzW7HarNis9lx2G3Y7DZqrTbqrFbUshstLjSSGx0uNLjQonzXSw4MODBix6xyEKmXiTK4iTR4CNO6CdG4sKidaD02JKdVcV/eYEx1xkBqAY+kwWmIwGWMxNxvMB5LLPagaGzmSKymUGyGEKyGIGwS2Fw2xkSPwaw1A/Bt3rd8ffprxkaP5ZpB1wCQW53L9euux+62t3VZ1JKaxOBERkSMYETECK4eeHWfXTMh6gv/I3Tsf3q6jl1uD7nlVo4W1ZBdVMWegu84XpVNmfMkTnUuKn0hksrVZh7WM3PQWycQbNSit+TgMH1LiCqJocaZBBk0BBu0lHrSMet1mDVGzDrlE6wzYdEbCNKbCNEbMen0GLRqDFoVOo0KjUrVIY+sPV3HfYUO6dlpbZy9UZ0PVWeaHOtne1QXtLy2uDNojPXGVpAyC0RrAq1BOWoMyr5eTc9pjUoabf1HrQW1TjmqmnxvOK/S+sZpGk+l9tu0x0CXZb+6Yj948CDDhw/3MawARo0a5Q1vzbg6ePAgl1xyyVnnG9JmZGQQHx/PwYMHfc43j7t161afPKOionwMq+bydISMjAwSExMJDg72nrPb7V5DMCwsjIQE30Xy2dnZ1NUpDdHmf3RJSQl5eXkAJCQk+Gx45na7vXIFBQUxaJDSu75yzx+plCuRtkso9q6MyjsKqNi/sqxMZwKQJImxDgsTHcGATJXk4j1TEVoPLKiKRKNVei/WG8vJVdvxyDIN88CkFiplj6cx32FOA1faFF048fB6UDHIcGdFGEaNku/nhiqydHaQZRrsc0mSkKSmu0jIyB7FD5skSQx06ZhV2+iB7ZXgUlzI3FIRRLhKj4TMFkMd3xlsZ+ULEkhNcm4YkZEg1q1hbnWju+w3giqpVnmYW2kiTtYhIbFTV8u3JgdIwHZv0vp88erG29cgQYhHzV3lZkX/soflIXUUatzcWKFhsEOFhIcDBhcbghucPsj1eSpHGVkRWQIJGaleM3pZ5snCGlR4UCHzRpiRTL2GWytruNimlKn9eh1LQptsWKsBnQZ0Zgg9699ruDr8rbCYhlVRb4UEscNo4MaqGqbVWKEGjms1PBgRDs4mCbX1H4sFUPQoS6r6jxpJo+VvqjjC9aFgCud1WwH/teUx1TiUBYNmEhwzkNOyg/lbf4fD5cAte3DLdjy2A7is30NxKwIDH8z6gJTwFAD25u3l/az3KSguYLxlPNHR0YQbwr2GlUVtIVwbTrg+nJR+KSQFJ5EQnEBicCJyhUxleSUAQ5KGYDI2Tquora3l6NGjAERFRREXF+cjQ2ZmJna7HY1Gw8iRI33CCgoKKCxUehwHDhwY0DqiAZdLadA5nU5cLpdPfVxRUcGpU8rGx3FxcURF+bqd379/P7IsYzQaGTp0qE/Y6dOnKSsrA5SOLIOh0WFJTU0Nx44pe39FR0cTGxvrk/bQoUPeF9+IESN8wvLz8ykqUvYZSk5OxmJpfFZtNhtZWVkAhIeHM2CA79q3I0eOYLVakSTprHdCcXExZ86cASAxMZHQ0MYnw+VykZGRAUBwcDADBw70SXv8+HHvizI1NdVnxkV5eTlOp/KANNSLTUlPTwfAZDIxZMgQn7CcnBzKy8sBGDZsmM8U9qqqKk6cOAFATEzMWe+tjIwMXC4Xer2eYcOG+YSdOXOG4mLlQRo8eDBms9kbVldXR3Z2NgARERH079/fJ21WVhY2mw21Wk1qaqpPWFFREfn5iue8pKQkQkIa6xyHw8Hhw4cBCAkJISkpySftsWPHqKlRPIimpaX5NDJKS0vJzc0FoH///kRERHjDPB4PBw4c8Oq4OSdPnqSyUnmWhw8fjk7XuM6zsrKSkydPAhAbG3vWGuyDBw/idrsxGAykpKT4hOXm5lJaWgrAkCFDMJnariM0ahVJkWaSIs30V5UzOWwYGk0qI0eOxOpwk1NWzb6CY3yfc4jjFSepcBVTJ5VhlUtwShXIqlpkVxC1Dje1DjcacjAG76K8ppLDWeO817YM/SuSuu0GtSyrwKMBVMiyGnvBtbirR6NWgcZ0Am3MWiRnHLqyW9GoJJDd2MPfRVZVI0kgIaHZowGU9oXynpNQSypUKjVKDAjzXIymWinTHl0pFeZP0RJConwzkiRht1nJU63FqSpDq9F4HYAo+Xq8dZNapULVZC1shGoMxpoReDwe3Kpaikz/RYWWFM2dgFIP5LjXY1PlodFokZqUJVn24KovKyqV2qe+C5VSCKq7ALfbjQcnBZaPlHKjuQuVpMFms3Pa+Rk1qhNoNBrUTfMFnA5F75JKhVaj6AcgSJVIuPVi7/2cMa9GxsNQ7c3opSDsDgenbV9TqTqMRqPB5XIhyzKSJKE/oMNhb8hXQqttHEkyStH0c/wYhz0CiKDQfAqXZCLZ/ADGoGicDgdFtVuoUO/FoHKjk9xoZCca2YFGdqBy2ZTfuNHiRoUbtewk0uXgd2VK2cZl5RWNjjOSk1tLTpFSr7s9Bj1rLI31RkfQyTKPlpZ7fy8NDiJbp+XG6lrG2ZX38mGdluXBje06DyqQfFtDynflI0sAEr8pcyHJStgnQRoy9Cous6q40K7Gg4pTkpv/BHuQJYnnbm9s90Ng6oiGd3lH6ZRxVVpaetaLHvBOvWsQqrW0zafotZS24dha3KbXaC1Ps9mMTqdrU56mNDwYTZFl2Vv5NzxgzdO09nLweDxtvpyb52symTimyuOY/qyobTLCdobx1cp+Q6c1anZFxGP0eHi16DDYlDhvmqLYYejcDuRxriIuqFUaWXWSxO5opcGzpOgIBruipw+MEew2dO5BNdWVM9baaPDui+6PXaXi6ZLjxLoVJwabjaHsMQS3lkWLpNmqGW1rHBHNioqjQKPhwfIsRtZXnrsNQXxv6tyUsHinjdHObO/vp/QxHNLr+XlVLiNlRcFZajPfmRoaDlKzY8sYPR7CpEa35kf0FrabDMysbVyLVK5SsdXU+Z3jPUkXgdYCWgOZtpNsl8tJMw7hsqhxGCyh1Liq2Xl6TSdzdWG78Q2wKEZJwTd/4eSJTHKN0dgTLoOoKKTqXMrs5W3molfr0Uk6NGjQq/SEmEJ81iuMDh/NrMhZDDINwl1fHkxaExtv3EikMZKM9Aw8Hg8Gg+GsRuKp8lPe56qtZ7kh36Y4nU6cTudZ6RridyRff9cRTVGr1d7zzWVqmm9r9yrLss8Lv4G27rUj+bZ2r03zbX6v7f03DTpsaW1cR/M9l/+mgZb01NF8z6UculyuFntCO1oO2/pvWgprK9+GtO3l2xIdLd8qlcqnAdNcpua0d68OhwOPx9Pi8oSu0GFDOqNOTUq/UFL6XcDFUf28BuqQIUO8BqrD5aC0qo496ZnUOmXK1BM4LYejlyLoP2o4VTYXJ8/ks9vdH6fbBio3bux4cCLjQJYadSBJHqg3wJS2qQcZcHlAxopWV4jLpaeqpnGE3xxzHJW2qvEeWtSoL8Ul/XGWKZ1EKkMZZstePI5wjh+b5o1jSjqEWp9Xr7hmGTRtUTYJyy3U4ShOVOTXlmMZvB3ZrSP70DXeOMYBmWgsR5QfzYtM03ybhOVW2LHl1zeQVXaCUrYBcHT/1SArz64h9ija0O87l29lKdbcxs4cS8p2JJWLowcvQXYpnTj66OPoInafnY+7hd8NX60DSD850fvbPHgnKm0lR4+OwWNT/iFdRAH66AO0SIsz/rR4HDG8YfsHFqxYJCt1xndwGko4XHENMY4IjNgpMp4kPehQy/m2gsEjc0uxHi1utJKLb4wGdpu0jLW6SLO50EpuCtUaPg7q/F6QTxSfQV9fRo5pIvjcZGa0tZQ4u9LpVarX8aVZ6YDySEo7uaEzMVB1RGfo9CbCbS0Ab29xeGfStha3o/E6Ik8DGo2mxXwbXqzNR+oazrX04gXlhdEQ1tKLsnm+Q4YM4Yp9VzLOWozD6cRTXyD0BkMTuSQ8bjcOhwMJUGt1REZEsaO+Z7pOdnJt3WFUSGyOm4UlSOlJGOPJZYBci8Ppwl3fGNAb9PWNWiVvj+zBbrODBFqNlgHhkeyMVnqmXbKbG2oOIMvwVdxMwkLCAIkhnjP8zFNV/9JR8jUY9Mr9SkovmMcjY7MpRohaoyYuLILd0Y29+9dW7cPldrMrdhZxYdEgQby7iFvcZTidThxOByBh0OtR1+uqYZCprq4OJKWhGR0exp6Ygd7h6KmV+7G67WT2i6cuPA6VSkW4q4QF7iLcLpdXJp3BgK5+JK7+jeXtiVWr1USEh7A/PkWZfiGpuKI8g7HOGsoS+pMZm4xOqyPaXc59ttM4XW5qa2qRJAmj2YzFbEZSqdCo1ahVaspKS5ABjUZLTHQ/mHmF4llIkrj26BZGl+diHjiY2uGTMQeFkGIr46nifdidbu/IicViOaszoSC/AIfTgUqlon///mgGXg0qRVdXZ31J0pnDJJmSsA+7CENICANs5Tx75ke4XC7yzigvSJPJRFSkUo4aylthYaFXTwMGDCBU3zgqcG3itSSrkonURXrLd4wphg9mfYBaUnMs+xhq1ARZghg8cDBGjRG9Wo9apW6zx2ls1FjCasO8+m8g3hKv/F86HW63u8XnTq1We8+39Sy3VKFqtVo8Hk+Lz3lH8/V3HdGUkJAQqqqqWpSpab6t3assy52+147k2/TYWr7N77W9/6ZBhy3V5R3N94f8N81Hl6Dt/6ZpvudSDpvGacoPLd9ut7vFsLbybUjbVr4/tHxbLBaSk5Nblak57d1rT6ojdBod4WaZhHClkywsLJ6EhKt90mZnS9TV/QU4e3S7uLiYk7kncXgcRMVGYbAYqHM6sbucBGvCyMnOwyXLuHVR2C0T0Uh6BgYPx+WWycnNY0/RbdhlOxERkXhQpqh7ZA82u43KqipkWcZkNmEwGPDIMjIe+qcMw16kxiODU22gWLcIncpE2thRIENpWRn7y3+MTa7GEhSESqVW9giUlY6FmvoOQr1ej7HJyHd0/GA0leG4PR7ckoFi452oUDM2RRnlrqyq4nDF5dTKozCbzT56drs91NQoDW6dVofR2NjpGB47AHNCpNIxIbspNt8BwJhrUlFJampqasgqm0yVPAij0eRTLmS5cZqXRqP1MfKDY6IJ6x+NvX50psB4K0gyI64ajV5los5ax5HSC6nwxGAwGrzvsYb9EqsqlXzVGpXPKLNZHUZ0bD+sVmWNcLFpLm7JTsqACzBrwrDZ7BwtKaPEY0Kv16E3+G53Ul1VjSzLqNQqnxkAOslEQmwCNTWK/stMc3FINST3n0SINgaHw4lclE6aZxhandZHh6DMTPC4PUgSBDWZnaFCzdqYK6iqUu4n2JjFRaoKsuPH8bYuAbfTycnC/Yxx70OnUWEy6AAZSfYgIWOts+JxO5GQsZhN9WHKWNbq4eOw1dYgyR7MhjNcra6gLqE/69X9kGQPOWU5XOk6ilqtQqPS+cwSOHnyZEDqiM7QqTVXkyZNwu12s2vXLp/zGRkZpKam8tprr3H33Xe3mDY2NpZLLrmEVatW+Zxfv349M2fOZNOmTUybNo1NmzYxffp01q9fzzXXXOMTd86cOWzdutU7FWTevHl88cUX3iknDdTW1mKxWHj44Yd56qmnfMJ64porgUAgEAgEAoFA0PPorO3QKYsiLS2Nw4cPnzUd4sABZQiz+VSd5mkb4rWVtuHYWtym10hLS6O4uJiCgoJOyyMQCAQCgUAgEAgEXUmnjKsbbriBmpoaPvzwQ5/zy5YtIy4ujokTJ7aSUkmbmZnp43Ld5XKxfPlyJk6c6F1kHh8fz4QJE1i+fLnPfMkdO3aQlZXF7Nmzveeuu+46JEli2bJlPtdaunQpRqOR6dOnd+b2BAKBQCAQCAQCgeCc6dSaq6uvvpqpU6eycOFCqqqqGDx4MCtXrmTjxo0sX77cO7/xzjvvZNmyZRw7dozERGUR4x133MErr7zCnDlzvJsIL1myhKysLDZv3uxznWeffZapU6cyZ84cFi1aRFFREQ899BCpqancfvvt3ngjR47kzjvv5NFHH0WtVnPhhRfy2Wef8frrr/PEE0+06OyiJ5KTk+NdqNfc45igaxA67h6Env2P0LH/ETr2P0LH/kfouHsQevY/vU3HnXZo8dFHH/GHP/yBRx55hLKyMoYNG8bKlSuZO3euN47b7cbtdvt419Dr9XzxxRc8+OCD3HvvvdTV1TFmzBg+/fRTLrvsMp9rXH755WzYsIFHHnmEWbNmYTKZmDlzJs8995yPa1tQNieOj4/npZdeoqCggKSkJF544QXuvffezt5awGhw/avVantFoemNCB13D0LP/kfo2P8IHfsfoWP/8//t3V9o1fUfx/HX5tEst8g5/3RkM7pIm00FwZ2BOnIshgY2QcLwX6IEKSaUSWp5hgpeFLTEP6nopE2LFSOiQEzbjX9SKmET6iYFKdRxwpgHlA7n/bvaar9zdvY95/v9nj/u+YBd+OHzOfucly+Pftz5fg8ZZwc5+6/QMk77cFVSUqKWlha1tLQMOae1tVWtra0J45MnT054C99QGhoa1NDQMOy80aNHKxwOKxwOO3pcAAAAAPBDWncLfBTk490CHz58+O8H0D2W5oddwREyzg5y9h8Z+4+M/UfG/iPj7CBn/+U643TPDhyulPvDFQAAAID84+ut2AEAAAAAyXG4AgAAAAAPpH1Di0KX7F2Q8Xg8Bzv5139/1FhaWprDnTy6yDg7yNl/ZOw/MvYfGfuPjLODnP2X64yTnRNSXVU14q65isViikajud4GAAAAgAI0btw4BQLJf0bF2wIBAAAAwAMcrgAAAADAAxyuAAAAAMADI+6aq3g8nnBhWlFRkYqKinK0IwAAAAD5yMwSbmBRXFzMhwgDAAAAgJ94WyAAAAAAeIDDFQAAAAB4gMNVDvT19endd9/VSy+9pIkTJ6qoqEjhcDitx7h7967Wrl2r8vJyPfHEE6qtrdW5c+f82XCBun//vrZs2aJgMKixY8dqzpw5+vzzzx2tbW1tHbgW7/+/bt++7fPO84ubHOmpc5nmTFedc/vaS5+H5yZjujy88+fPa926dZoxY4bGjRunqVOnaunSpfrpp58crafDzrjJmR47c+3aNS1ZskSVlZV6/PHHVVZWptraWrW1tTlan89dTv7pV/BVJBLRkSNHNHv2bL3yyis6duxYWusfPnyo+vp63bt3Ty0tLZo0aZIOHDigxsZGff/996qrq/Np54Vl2bJlunr1qvbt26fnnntOp06d0ooVKxSPx/Xaa685eowTJ05oxowZg8YmTJjgx3bzVqY50tP0uO0rXR2em9de+uyM27/fJLqcyqFDhxSJRPTWW2+pqqpKvb29+uijjxQKhXTmzBktWrRoyLV02Dk3Ofejx6ndu3dPFRUVWrFihaZOnapoNKr29natWrVKN2/e1M6dO4dcm/ddNmRdPB63eDxuZma9vb0myXbt2uV4/YEDB0ySXbx4cWDsn3/+saqqKps3b57X2y1I3377rUmyU6dODRpvaGiwYDBosVgs5foTJ06YJLt69aqf28x7bnKkp865yZmuOufmtZc+O+MmY7o8vDt37iSM9fX12eTJk62+vj7lWjrsnJuc6bE7NTU1VlFRkXJOvneZtwXmgNtbv3d2dmr69Omqra0dGAsEAlq5cqWuXLmiP/74w4ttFrTOzk6VlJRo+fLlg8Zff/11/fnnn/rxxx9ztLPC4iZHeuocfc0ON6+99NkZPtrEX5MmTUoYKykpUVVVlW7dupVyLR12zk3OcKe8vFyBQOo31uV7lzlcFaCenh7NmjUrYbx/7Pr169neUt7p6enR888/n/AHtD+jnp4eR4/z8ssva9SoUSorK9OyZcscr3tUuMmRnjrnRV9Helf9Rp+zhy6n5++//9bPP/+smTNnppxHh91xmnM/euxMPB5XLBZTb2+vDh48qDNnzmjbtm0p1+R7l7nmqgBFIhGVlZUljPePRSKRbG8p70QiET377LMJ404zmjJlinbs2KFQKKQnn3xS3d3d2rdvn0KhkC5cuKDZs2f7su984yZHeuqcm5zpanbQZ//R5cxs3LhR0WhUO3bsSDmPDrvjNGd6nJ4333xTn376qSRpzJgx+uSTT/TGG2+kXJPvXeZw5VJXV5defPFFR3N/+eUXzZkzx5Pvm+ptF4/aWzIyzdhNRo2NjWpsbBz49cKFC7VkyRJVV1frgw8+0Ndff+1oP48CNzmOpJ66lWlWdDV76LO/6HL63n//fbW3t2v//v2aO3fusPPpcGbSyZkep2f79u1av3697t69q2+++UabNm1SNBrVO++8k3JdPneZw5VL06dP19GjRx3Nrays9OR7TpgwIemp/K+//pKkpKf5QpZJxn5k9Mwzz2j+/Pm6fPly2msLlZscR1pP3fA6q5HYVb/R59ygy0Nrbm7Wnj17tHfvXm3atGnY+XQ4M+nmnAw9HlplZeXAv90WL14sSXrvvfe0Zs0aTZw4MemafO8yhyuXnn76aa1fvz6r37O6ulrd3d0J4/1jL7zwQlb347dMMq6urtbp06cVi8UGXcfiNiMzU3HxyLlU0U2OI62nbvjR15HWVb/R59yhy4mam5sVDocVDoe1fft2R2vocPoyyXko9NiZefPm6fDhw/r999+HPFzle5f5XS5ATU1N+vXXXwfdQSwWi6mtrU01NTUKBoM53F1+aGpq0v379/XVV18NGj958qSCwaBqamrSfswbN27owoULCoVCXm0z77nJkZ4653VfR2JX/Uafc4MuJ9q9e7fC4bB27typXbt2OV5Hh9OTac7J0GPnfvjhBxUXFye9Drlf3nc5t3eCH7m+++476+josOPHj5skW758uXV0dFhHR4dFo9GBeevWrbNRo0bZzZs3B8YePHhgM2fOtIqKCmtvb7ezZ89aU1OTBQIB6+rqysXTyUsNDQ02fvx4O3LkiJ0/f942bNhgkqytrW3QvGQZ19fXW3Nzs3V2dtq5c+fs448/tmAwaKWlpdbd3Z3tp5JTTnKkp+5lmjNdTY+T11767E6mGdPl4X344YcmyRobG+3SpUsJX/3osDtucqbHzmzYsMHefvtt++KLL6yrq8u+/PJLe/XVV02Sbd26dWBeIXaZw1WOTJs2zSQl/bpx48bAvDVr1iSMmZndvn3bVq9ebWVlZTZ27FgLhUJ29uzZ7D6JPNfX12ebN2+2KVOm2JgxY2zWrFl2+vTphHnJMt6yZYtVVVVZaWmpBQIBCwaDtnLlSvvtt9+y+Azyg5Mc6al7meZMV9Pj5LWXPruTacZ0eXh1dXVDZvvf/y+nw+64yZkeO3P8+HFbsGCBlZeXWyAQsKeeesrq6urss88+GzSvELtcZGbm9U/DAAAAAGCk4ZorAAAAAPAAhysAAAAA8ACHKwAAAADwAIcrAAAAAPAAhysAAAAA8ACHKwAAAADwAIcrAAAAAPAAhysAAAAA8ACHKwAAAADwAIcrAAAAAPAAhysAAAAA8MD/AHQ6fv/7NwfqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d91792c080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-1, 3, 0.01)\n",
    "g1 = gaussian(x, mean=0.8, var=.1)\n",
    "g2 = gaussian(x, mean=1.3, var=.2)\n",
    "plt.plot(x, g1, x, g2)\n",
    "\n",
    "g = g1 * g2  # element-wise multiplication\n",
    "g = g / sum(g)  # normalize\n",
    "plt.plot(x, g, ls='-.');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here I created two Gaussians, g1=$\\mathcal N(0.8, 0.1)$ and g2=$\\mathcal N(1.3, 0.2)$ and plotted them. Then I multiplied them together and normalized the result. As you can see the result *looks* like a Gaussian distribution.\n",
    "\n",
    "Gaussians are nonlinear functions. Typically, if you multiply a nonlinear equations you end up with a different type of function. For example, the shape of multiplying two sins is very different from `sin(x)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d9175e2eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0, 4*np.pi, 0.01)\n",
    "plt.plot(np.sin(1.2*x))\n",
    "plt.plot(np.sin(1.2*x) * np.sin(2*x));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But the result of multiplying two Gaussians distributions is a Gaussian function. This is a key reason why Kalman filters are computationally feasible. Said another way, Kalman filters use Gaussians *because* they are computationally nice. \n",
    "\n",
    "The product of two independent Gaussians is given by:\n",
    "\n",
    "$$\\begin{aligned}\\mu &=\\frac{\\sigma_1^2\\mu_2 + \\sigma_2^2\\mu_1}{\\sigma_1^2+\\sigma_2^2}\\\\\n",
    "\\sigma^2 &=\\frac{\\sigma_1^2\\sigma_2^2}{\\sigma_1^2+\\sigma_2^2} \n",
    "\\end{aligned}$$\n",
    "\n",
    "The sum of two Gaussians is given by\n",
    "\n",
    "$$\\begin{gathered}\\mu = \\mu_1 + \\mu_2 \\\\\n",
    "\\sigma^2 = \\sigma^2_1 + \\sigma^2_2\n",
    "\\end{gathered}$$\n",
    "\n",
    "At the end of the chapter I derive these equations. However, understanding the deriviation is not very important."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Putting it all Together\n",
    "\n",
    "Now we are ready to talk about Gaussians can be used in filtering. In the next chapter we will implement a filter using Gaussins. Here I will explain why we would want to use Gaussians.\n",
    "\n",
    "In the previous chapter we represented probability distributions with an array. We performed the update computation by computing the element-wise product of that distribution with another distribution representing the likelihood of the measurement at each point, like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d9166a3da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def normalize(p):\n",
    "    return p / sum(p)\n",
    "\n",
    "def update(likelihood, prior):\n",
    "    return normalize(likelihood * prior)\n",
    "\n",
    "prior =      normalize(np.array([4, 2, 0, 7, 2, 12, 35, 20, 3, 2]))\n",
    "likelihood = normalize(np.array([3, 4, 1, 4, 2, 38, 20, 18, 1, 16]))\n",
    "posterior = update(likelihood, prior)\n",
    "book_plots.bar_plot(posterior)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In other words, we have to compute 10 multiplications to get this result. For a real filter with large arrays in multiple dimensions we'd require billions of multiplications, and vast amounts of memory. \n",
    "\n",
    "But this distribution looks like a Gaussian. What if we use a Gaussian instead of an array? I'll compute the mean and variance of the posterior and plot it against the bar chart."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean: 5.88 var: 1.24\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d9166a3e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.arange(0, 10, .01)\n",
    "\n",
    "def mean_var(p):\n",
    "    x = np.arange(len(p))\n",
    "    mean = np.sum(p * x,dtype=float)\n",
    "    var = np.sum((x - mean)**2 * p)\n",
    "    return mean, var\n",
    "\n",
    "mean, var = mean_var(posterior)\n",
    "book_plots.bar_plot(posterior)\n",
    "plt.plot(xs, gaussian(xs, mean, var, normed=False), c='r');\n",
    "print('mean: %.2f' % mean, 'var: %.2f' % var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is impressive. We can describe an entire distribution of numbers with only two numbers. Perhaps this example is not persuasive, given there are only 10 numbers in the distribution. But a real problem could have millions of numbers, yet still only require two numbers to describe it.\n",
    "\n",
    "Next, recall that our filter implements the update function with\n",
    "```python\n",
    "def update(likelihood, prior):\n",
    "    return normalize(likelihood * prior)\n",
    "```\n",
    "\n",
    "If the arrays contain a million elements, that is one million multiplications. However, if we replace the arrays with a Gaussian then we would perform that calculation with\n",
    "\n",
    "$$\\begin{aligned}\\mu &=\\frac{\\sigma_1^2\\mu_2 + \\sigma_2^2\\mu_1}{\\sigma_1^2+\\sigma_2^2}\\\\\n",
    "\\sigma^2 &=\\frac{\\sigma_1^2\\sigma_2^2}{\\sigma_1^2+\\sigma_2^2} \n",
    "\\end{aligned}$$\n",
    "\n",
    "which is three multiplications and two divisions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayes Theorem\n",
    "\n",
    "In the last chapter we developed an algorithm by reasoning about the information we have at each moment, which we expressed as discrete probability distributions. In the process we discovered [*Bayes' Theorem*](https://en.wikipedia.org/wiki/Bayes%27_theorem). Bayes theorem tells us how to compute the probability of an event given prior information. \n",
    "\n",
    "We implemented the `update()` function with this probability calculation:\n",
    "\n",
    "$$ \\mathtt{posterior} = \\frac{\\mathtt{likelihood}\\times \\mathtt{prior}}{\\mathtt{normalization}}$$ \n",
    "\n",
    "It turns out that this is Bayes' theorem. In a second I will develop the mathematics, but in many ways that obscures the simple idea expressed in this equation. We read this as:\n",
    "\n",
    "$$ updated\\,knowledge = \\big\\|likelihood\\,of\\,new\\,knowledge\\times prior\\, knowledge \\big\\|$$\n",
    "\n",
    "where $\\| \\cdot\\|$ expresses normalizing the term.\n",
    "\n",
    "We came to this with simple reasoning about a dog walking down a hallway. Yet, as we will see, the same equation applies to a universe of filtering problems. We will use this equation in every subsequent chapter.\n",
    "\n",
    "\n",
    "To review, the *prior* is the probability of something happening before we include the probability of the measurement (the *likelihood*) and the *posterior* is the probability we compute after incorporating the information from the measurement.\n",
    "\n",
    "Bayes theorem is\n",
    "\n",
    "$$P(A \\mid B) = \\frac{P(B \\mid A)\\, P(A)}{P(B)}$$\n",
    "\n",
    "$P(A \\mid B)$ is called a [*conditional probability*](https://en.wikipedia.org/wiki/Conditional_probability). That is, it represents the probability of $A$ happening *if* $B$ happened. For example, it is more likely to rain today compared to a typical day if it also rained yesterday because rain systems usually last more than one day. We'd write the probability of it raining today given that it rained yesterday as $P$(rain today $\\mid$ rain yesterday).\n",
    "\n",
    "\n",
    "I've glossed over an important point. In our code above we are not working with single probabilities, but an array of probabilities - a *probability distribution*. The equation I just gave for Bayes uses probabilities, not probability distributions. However, it is equally valid with probability distributions. We use a lower case $p$ for probability distributions\n",
    "\n",
    "$$p(A \\mid B) = \\frac{p(B \\mid A)\\, p(A)}{p(B)}$$\n",
    "\n",
    "In the equation above $B$ is the *evidence*, $p(A)$ is the *prior*, $p(B \\mid A)$ is the *likelihood*, and $p(A \\mid B)$ is the *posterior*. By substituting the mathematical terms with the corresponding words  you can see that Bayes theorem matches out update equation. Let's rewrite the equation in terms of our problem. We will use $x_i$ for the position at *i*, and $z$ for the measurement. Hence, we want to know $P(x_i \\mid z)$, that is, the probability of the dog being at $x_i$ given the measurement $z$. \n",
    "\n",
    "So, let's plug that into the equation and solve it.\n",
    "\n",
    "$$p(x_i \\mid z) = \\frac{p(z \\mid x_i) p(x_i)}{p(z)}$$\n",
    "\n",
    "That looks ugly, but it is actually quite simple. Let's figure out what each term on the right means. First is $p(z \\mid x_i)$. This is the the likelihood, or the probability for the measurement at every cell $x_i$. $p(x_i)$ is the *prior* - our belief before incorporating the measurements. We multiply those together. This is just the unnormalized multiplication in the `update()` function:\n",
    "\n",
    "```python\n",
    "def update(likelihood, prior):\n",
    "    posterior = prior * likelihood   # p(z|x) * p(x)\n",
    "    return normalize(posterior)\n",
    "```\n",
    "\n",
    "The last term to consider is the denominator $p(z)$. This is the probability of getting the measurement $z$ without taking the location into account. It is often called the *evidence*. We compute that by taking the sum of $x$, or `sum(belief)` in the code. That is how we compute the normalization! So, the `update()` function is doing nothing more than computing Bayes' theorem.\n",
    "\n",
    "The literature often gives you these equations in the form of integrals. After all, an integral is just a sum over a continuous function. So, you might see Bayes' theorem written as\n",
    "\n",
    "$$p(A \\mid B) = \\frac{p(B \\mid A)\\, p(A)}{\\int p(B \\mid A_j) p(A_j) \\,\\, \\mathtt{d}A_j}\\cdot$$\n",
    "\n",
    "This denominator is usually impossible to solve analytically; when it can be solved the math is fiendishly difficult. A recent [opinion piece ](http://www.statslife.org.uk/opinion/2405-we-need-to-rethink-how-we-teach-statistics-from-the-ground-up)for the Royal Statistical Society called it a \"dog's breakfast\" [8].  Filtering textbooks that take a Bayesian approach are filled with integral laden equations with no analytic solution. Do not be cowed by these equations, as we trivially handled this integral by normalizing our posterior. We will learn more techniques to handle this in the **Particle Filters** chapter. Until then, recognize that in practice it is just a normalization term over which we can sum. What I'm trying to say is that when you are faced with a page of integrals, just think of them as sums, and relate them back to this chapter, and often the difficulties will fade. Ask yourself \"why are we summing these values\", and \"why am I dividing by this term\". Surprisingly often the answer is readily apparent. Surprisingly often the author neglects to mention this interpretation.\n",
    "\n",
    "It's probable that the strength of Bayes' theorem is not yet fully apparent to you. We want to compute $p(x_i \\mid Z)$. That is, at step i, what is our probable state given a measurement. That's an extraordinarily difficult problem in general. Bayes' Theorem is general. We may want to know the probability that we have cancer given the results of a cancer test, or the probability of rain given various sensor readings. Stated like that the problems seem unsolvable.\n",
    "\n",
    "But Bayes' Theorem lets us compute this by using the inverse  $p(Z\\mid x_i)$, which is often straightforward to compute\n",
    "\n",
    "$$p(x_i \\mid Z) \\propto p(Z\\mid x_i)\\, p(x_i)$$\n",
    "\n",
    "That is, to compute how likely it is to rain given specific sensor readings we only have to compute the likelihood of the sensor readings given that it is raining! That's a ***much*** easier problem! Well, weather prediction is still a difficult problem, but Bayes makes it tractable. \n",
    "\n",
    "Likewise, as you saw in the Discrete Bayes chapter, we computed the likelihood that Simon was in any given part of the hallway by computing how likely a sensor reading is given that Simon is at position `x`. A hard problem becomes easy. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Total Probability Theorem\n",
    "\n",
    "We now know the formal mathematics behind the `update()` function; what about the `predict()` function? `predict()` implements the [*total probability theorem*](https://en.wikipedia.org/wiki/Law_of_total_probability). Let's recall what `predict()` computed. It computed the probability of being at any given position given the probability of all the possible movement events. Let's express that as an equation. The probability of being at any position $i$ at time $t$ can be written as $P(X_i^t)$. We computed that as the sum of the prior at time $t-1$ $P(X_j^{t-1})$ multiplied by the probability of moving from cell $x_j$ to $x_i$. That is\n",
    "\n",
    "$$P(X_i^t) = \\sum_j P(X_j^{t-1})  P(x_i | x_j)$$\n",
    "\n",
    "That equation is called the *total probability theorem*. Quoting from Wikipedia [6] \"It expresses the total probability of an outcome which can be realized via several distinct events\". I could have given you that equation and implemented `predict()`, but your chances of understanding why the equation works would be slim. As a reminder, here is the code that computes this equation\n",
    "\n",
    "```python\n",
    "for i in range(N):\n",
    "    for k in range (kN):\n",
    "        index = (i + (width-k) - offset) % N\n",
    "        result[i] += prob_dist[index] * kernel[k]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing Probabilities with scipy.stats\n",
    "\n",
    "In this chapter I used code from [FilterPy](https://github.com/rlabbe/filterpy) to compute and plot Gaussians. I did that to give you a chance to look at the code and see how these functions are implemented.  However, Python comes with \"batteries included\" as the saying goes, and it comes with a wide range of statistics functions in the module `scipy.stats`. So let's walk through how to use scipy.stats to compute statistics and probabilities.\n",
    "\n",
    "The `scipy.stats` module contains a number of objects which you can use to compute attributes of various probability distributions. The full documentation for this module is here: http://docs.scipy.org/doc/scipy/reference/stats.html. We will focus on the  norm variable, which implements the normal distribution. Let's look at some code that uses `scipy.stats.norm` to compute a Gaussian, and compare its value to the value returned by the `gaussian()` function from FilterPy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.13114657203397997\n",
      "0.13114657203397995\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "import filterpy.stats\n",
    "print(norm(2, 3).pdf(1.5))\n",
    "print(filterpy.stats.gaussian(x=1.5, mean=2, var=3*3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The call `norm(2, 3)` creates what scipy calls a 'frozen' distribution - it creates and returns an object with a mean of 2 and a standard deviation of 3. You can then use this object multiple times to get the probability density of various values, like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pdf of 1.5 is       0.1311\n",
      "pdf of 2.5 is also  0.1311\n",
      "pdf of 2 is         0.1330\n"
     ]
    }
   ],
   "source": [
    "n23 = norm(2, 3)\n",
    "print('pdf of 1.5 is       %.4f' % n23.pdf(1.5))\n",
    "print('pdf of 2.5 is also  %.4f' % n23.pdf(2.5))\n",
    "print('pdf of 2 is         %.4f' % n23.pdf(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The documentation for  [scipy.stats.norm](http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.normfor) [2] lists many other functions. For example, we can generate $n$ samples from the distribution with the `rvs()` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 5.912 -2.009 -2.718  1.266 -1.085  3.941  3.499\n",
      "  5.626 -0.137  1.396  4.562  2.127  8.176  1.794\n",
      "  1.829]\n"
     ]
    }
   ],
   "source": [
    "np.set_printoptions(precision=3, linewidth=50)\n",
    "print(n23.rvs(size=15))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can get the [*cumulative distribution function (CDF)*](https://en.wikipedia.org/wiki/Cumulative_distribution_function), which is the probability that a randomly drawn value from the distribution is less than or equal to $x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5\n"
     ]
    }
   ],
   "source": [
    "# probability that a random value is less than the mean 2\n",
    "print(n23.cdf(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can get various properties of the distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variance is 9.0\n",
      "standard deviation is 3.0\n",
      "mean is 2.0\n"
     ]
    }
   ],
   "source": [
    "print('variance is', n23.var())\n",
    "print('standard deviation is', n23.std())\n",
    "print('mean is', n23.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Limitations of Using Gaussians to Model the World\n",
    "\n",
    "Earlier I mentioned the *central limit theorem*, which states that under certain conditions the arithmetic sum of any independent random variable will be normally distributed, regardless of how the random variables are distributed. This is important to us because nature is full of distributions which are not normal, but when we apply the central limit theorem over large populations we end up with normal distributions. \n",
    "\n",
    "However, a key part of the proof is “under certain conditions”. These conditions often do not hold for the physical world. For example, a kitchen scale cannot read below zero, but if we represent the measurement error as a Gaussian the left side of the curve extends to negative infinity, implying a very small chance of giving a negative reading. \n",
    "\n",
    "This is a broad topic which I will not treat exhaustively. \n",
    "\n",
    "Let's consider a trivial example. We think of things like test scores as being normally distributed. If you have ever had a professor “grade on a curve” you have been subject to this assumption. But of course test scores cannot follow a normal distribution. This is because the distribution assigns a nonzero probability distribution for *any* value, no matter how far from the mean. So, for example, say your mean is 90 and the standard deviation is 13. The normal distribution assumes that there is a large chance of somebody getting a 90, and a small chance of somebody getting a 40. However, it also implies that there is a tiny chance of somebody getting a grade of -10, or 150. It assigns an extremely small chance of getting a score of $-10^{300}$ or $10^{32986}$. The tails of a Gaussian distribution are infinitely long.\n",
    "\n",
    "But for a test we know this is not true. Ignoring extra credit, you cannot get less than 0, or more than 100. Let's plot this range of values using a normal distribution to see how poorly this represents real test scores distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d91793a518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.arange(10, 100, 0.05)\n",
    "ys = [gaussian(x, 90, 30) for x in xs]\n",
    "plt.plot(xs, ys, label='var=0.2')\n",
    "plt.xlim(0, 120)\n",
    "plt.ylim(-0.02, 0.09);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The area under the curve cannot equal 1, so it is not a probability distribution. What actually happens is that more students than predicted by a normal distribution get scores nearer the upper end of the range (for example), and that tail becomes “fat”. Also, the test is probably not able to perfectly distinguish minute differences in skill in the students, so the distribution to the left of the mean is also probably a bit bunched up in places. \n",
    "\n",
    "Sensors measure the world. The errors in a sensor's measurements are rarely truly Gaussian. It is far too early to be talking about the difficulties that this presents to the Kalman filter designer. It is worth keeping in the back of your mind the fact that the Kalman filter math is based on an idealized model of the world.  For now I will present a bit of code that I will be using later in the book to form distributions to simulate various processes and sensors. This distribution is called the [*Student's $t$-distribution*](https://en.wikipedia.org/wiki/Student%27s_t-distribution). \n",
    "\n",
    "Let's say I want to model a sensor that has some white noise in the output. For simplicity, let's say the signal is a constant 10, and the standard deviation of the noise is 2. We can use the function `numpy.random.randn()` to get a random number with a mean of 0 and a standard deviation of 1. I can simulate this with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.random import randn\n",
    "def sense():\n",
    "    return 10 + randn()*2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot that signal and see what it looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2FgBw4YUXYtq0aZJni4uLEQgEkJ6ejoULF0quNTc3o6OjAwAwb948jB0bcWkaGhpCZWUlAGDy5MmYOXOm5NlAIKw0/X4/5LS3t6OlpQUAkJeXh+zsbOGaz+dDaWkpACA7Oxt5eXmSZ6urqzEwMAAAWLp0qSRqSldXFxobGwEAM2fOxOTJk4VroVAIZ86cAQCMGzcOc+fOlaRbV1eH3t5waOlFixZhzJgxwrXe3l7U1dUBAKZPn46pU6dKni0qKkIwGERGRgYWLFgQ9b21dbUo8Ldi/vz5yMrKEn4fHBxEVVUVACAnJwczZsyQPFdWVgav14vU1FQsXrxYcq21tRVtbW0AgNmzZ8dMR/DU1NRIdEQwxKFzwKeoI3p6enD27FkA6jqClxsxpCPCjDYdUV5eDo/HA7fbjSVLlkiuiXWEHC0dIe6rkkFHNDY2oqurCwBGhY4QjyPk1NbWoq8vvOpjVkfYPY7gdQ5L95yvOkIOr/sLC8/g4hnTEk5HxGscISceOoJvp0ZwxOgJhUIAwg1j06ZNyM3NBQBcc801uOKKK/Dggw9qGj2BQCDKwuY4ThhIshppIBBgDjT5PPHX+PyJYaWblZWFQCAAr9crXBfniffy46+JB0bidDmOQ1patH9oMBhkpivPr1K6St8qTlf+reIyZKXLlyHLhXH9qVZsONWKx741WTXdWNQNK101eVEqw0AgwAy5qFY3Wum6XC7F2SG1dPk8qeXXahmynhfnSY7Wt/p8PoRCIUnnI0k7EBTagJF0+W9llZHeurFbDsVpsLDSljmOQ0pKCrKysiSDoWTTEXrTPd91BF83rGtq7ZF/Vp4u31d5PJ6k0hF2lGEi6Yj6c8MYn56CzMzMqI3vanKoV0fYPY5Q43zVEUootdd464h4jSN4ncP3V/HSEUZxxOjhrcOFCxcKBg8QHgx++9vfxqOPPor29vYoa0+SsdTUqAbjcrmERi9fbeF/YykFAEhJSRGusYSTlS4/GyCeoRHniS9v/llWhaWlpYHjOGZ+3W638Kz8W8X5VUpX/LdSuvJvFZchK12+DFnK6vFd9cI71dKNRd2w0lWTF6UyFN8jRq1utNIdO3asMENjJF0+T2r5tVqGWt8qR+tbx4wZg2AwqPi8O9XNlCc9dRMKhQy3GyflUJwGCyttWWkWN9l0hN50z3cdkZaWhmAwqKkjWLDS5fsq8SyunETUEVbLMNF0xK+2dmHG+FS8+S9TAHgV0zWrI+weR2RmZgqrwWrpJqKOaOn14Gt/2oNPf/U1LLko2zYdoURaWlpC6oh4jSPkq8Hx0hFGcXEWHBY7OzuRk5OD+++/X3JWTyAQQHZ2NubNmycsKfLce++9eOyxx9DR0SEsP4ZCIWHJkmf8+PEJf+jRFQ/vQOeAF3WPnR8R6fJWbASA8+Z7CfOs2lWJJ7dVYM2Pr8DVl14Y7+zYgpL8U7sgnIDkKvkQ19nvPjyDNw/XC4Nywl52lLThZ387jt9+ewF++c15tqUrb3e3vHgAJ+t7UPbQdchIY3s0EPHBjO3giFWRmpqK7373uygtLRX8+IDwUtSWLVswd+7cpDvQiCAIgiAIQg+uURnD8vyDwhiMLky5t23evBmDg4OChVVSUoL169cDAG644QZkZWXhoYcewubNm3Hddddh5cqVmDBhAtasWYOCggK899579n0BQRAEQRBEAkGHWRJE4mHK6PnFL34hRBoBgHXr1mHdunUAwvtf8vLyMHfuXOzbtw8rVqzAnXfeCb/fj8svvxwff/wxbrrpJnty7zD19fXCRi15hBcgEsiAIMRoyc35BHX7+iG5IcxCskOYgeSGMEuyyo4po0fssqbGkiVL8Omnn5p5RULQ3d0tbPJjVWqihG9v6R2GCy5My87QvplwHC25OR8ws8HwfIfkhjALyU7iEm9V+OKeKnAcmPteSG4IsySr7CR2pABCF19+dBe+9OjOeGdD4N/fOI4fv3o03tkgCIIgEozOAS/yVmzEnvL2eGclJsR7cvRPW8rxxNby+GYiiYl3/RH24kjI6tHCwoULwXEczVobZGtxW7yzEFdIbgg5wRCH1w7U4tav5CHNzZ5rIrkhzJJMstPUPQwA2F3WjqsWKB9bQThPMslNvCHjR0qyyg4ZPSqIT+4mCL2Q3BByNhe14OGNpRibnop/uZLtCkByQ5jFSdkZ8gWwvaQN3738IsfeQcQH0jmEWZJVdsi9jSAIwmF8gZDkb4JIFh7fXIa73zmN5p5hW9M9XybOk2winCBGNWT0ELZR2zkIjz8Y72wQMeLcoA+D3kC8swEAGPAG8Ot3TmEgQfJDEKOFnmE/gLCLph2QEUAQRLwg9zYV+vr6BJ/FCRMmxDs7Cc83n9yDm/NnxDsbced8kZvPPbQdF03MxIEV/6R4DxcjR+iNhc348HQzvjhnsqL7WCLBcRw6B3zIGR9xEThf5EaN3mE/Spr78OW5k+OdlaTCSdmhvQzmSIZyI52jDSf8nQQVGkOSVXZopUeF2tpaVFZWora2Nt5ZSRoKGnrinYW4k0hyw3EcvvfiARyrO+dI+k02u7yMVuSz22v21eILj+xA78gsOpBYchMv/vPtU/iXlw/HOxtJh52y0zngZf5+btBnOW0isSCdQ5glWWWHjB7CVsh1IbEIhjicqu/B45vL4p0VQsSJs90AgGEfuYOKaeweincWzmuKmnpxxcM78FlFh/Abb5j/7sOieGUrKaG+kCASD3JvU+HCCy9EMBiE2+22nJY/GMKQL4jszDQbcpa4kJ63V26sEhzxsUg5z3vg3eXt2FXajoeWLYl3VhRJJLkhkgu7ZOdsV9joLG/tx9cvyQEQce/xBshAH20ks845z7u0uJOsskNGjwrTpk2zLa1fv3saGwtbUPfYjbalSSQmdsqNVXi/8pRRvqar5T9/+2vHACChjZ5EkhszdA54MXnsGFvPbfjKozvxgysuxm+uucS2NEcjdsmO2r4Fu/eoJMOeFyskw/dZlZuq9n4cre3Gj76Y+PsoTTNSkYlYn73DfoxxpyBzTOwNj2Ttr0b5UChx2G7jgZ09Qz7bIunYjdMHVVF0OGOEaKWHiAGdA15c8fAOvHW03tZ0m3s9eHZnpa1pEvHFRf4Ao4bv/+UQ7vvgTLyzcd6S/8A23PDcvnhnI6kgoycJufzB7Xh0U2lM37m9RJ/R5mR3tu54Axb+fotk8zehDm8bk9FDOEnPUHiT+6l6c4FMqE0nBrxBwoHDp4XNCCXo5FoiUds5OOpc//6ypxp5KzZq3kfnjsWf2s7BeGchqSCjJ0nZV9kZ0/c1nIv/BuP9VeFv7rNpgPSrt0/h9teO2pJWosKvCMbL5qEhk7N0DnjR3u+JdzYEzLiAnO0aRP4D27C1uNX+DBGG4N3b9lZ04K63TmHDyUZbJ7JGYwS4bz65B3/4sDgu735mRwVKmvtsT3ftweSJyBWrYxHspqq9H/5gbIzGyx/chhUbCmPyrkSHjB4ViouLcfr0aRQXG1doZa19yFuxEUVNvQ7kLIFJogWFTwqasbu8Q/tGg1iRG7vh4uTeRgtLbNQ6aDNyc8XDO3DlIzvtyFrc4MOeFzbGJtx93oqNeHzL6IpmaLfOGfCED/nt99h32G9rrwefe2g7NpxstC3NRKEgRrIr55kdlbh9rfmJu0TqqxIdO00rbyCIq5/+DI/piKraO+S3bBz1DPnxzrEGS2nISVbZIaNHhUAgIPwxSnFTePblZH233dkCkLiDylhkK9EnduRy0zXgxapdlXGZkeJXelISVF7OF/TsY7Cib0YDsWwe79o8AIg3tsuOi3dzi2C1evjzf06PwrPcEnWPrRZKcpPofawYp/cROwEvL6Ut2qt0+Q9uw2/ePe10lgyTrP0VGT0qpKenC3+MkuoON8RA0Lz2GPYF8eftFQmhUJNQr8QNudw8+GkJntxWgZbeiBvSyo+Lcbimy/G88KLjJqsn4bGib+LNkIXzhiL7SJyjd8iPd2wOspBI2C07vLZwcqJmNJ1wH1Qpp0QO3JDMOocnWd3bjLCztD3eWYgiWWWHQlarsHDhQtPPpo7ECA6EzC9LvnqgFs/urMTlF0/ENxdONZ1OLDEz6+INBLHy4xKsuH6hrnOMEt0Ak8tNgGG0rj1Yh/UnGlH0wLcdzQsfvU2rXn669hi+c/kMfPfyixzND6GMFX0Tb76z6gCAxB3I/v6jInxc0IzrliRnmFUt7JYdXl2EOC7h9W0ioBbwIVHbBKAsN3bVOcdx2FPegasW5CTligxA+1KVSNb+ilZ6HEJY6bGwSsOv8ISSYCbDymzLgapOvH20Hm8cqtP5LtOvSihiMUMVCVmtft/Osnbc/Y79S+ixrqvk7FYJHqcGRgPesAvGaNEdseKPmyJ7Ds6HGXWzqK30WOGTgmbkrdgY86Ma7PqcD0834fa1xxwNvBQrY4rkf3RARo9DpI6MMoMW3NuSaQDH23bJlOfzgcienhgHMiBJYDLau00z9S4WTRpYEJ0DXmwsbIl3NgxhxqHj0U2lmmGhPzzVBAAY9CbXvgmeroFwtL4eB0PSO60zSCWNLsjocQh+D4WVlZ5kghPcqOKckSQiFpLBK+yUUbCnJxjiaFCc4CSyKw+hn3hqi/948yR++dbJOObAOGreGEoTAetOjL4odnISzaXt4U9LdJ0/5DRGu7FYF2MoxCEQo3DasYb29KjQ3NyMYDAIt9uNGTNmGHo2zW19T08iodXmYjnUSTA9GoUVubGbeK30OMHc+zbhB5+fiSd+kB/vrDhCIslNPCB7NsygN4DF92819EwyyI5eFdQ9lHxn+TgdbMip1JNBbszQNeDF5HHRG+z/fkR/MJNjdecwf+o4O7OVNPz41aPYX9WJusduVLwnWWWHVnpU6OjoQFtbGzo6jJ/lcv6t9IT/joVbU6IPjsRy4wuEFF0cY/EdQiAD51+lgL0fOZpnR63om2RGLJuJNjMcD8wc4GmX7LB0khDJzVLK+t4FJP6kFgvWSo9WeSXCZ1qVG7115cQKvdK7zzT24vMP78CBquh9REZk6wcvHcKdfzthMnfJzX5G2clJ1v6KjB6HEGbWE3yAzqK6YwC/ePOEodkr3q3FyQ4rEToJo1zyu83YEseT5vkajPVAItbvS8Jmdt5wsr4bDeeGNO/j4Jz7IrnfGoNlfNpVdKOxDpye20zWInMy30qqoq5rEABQ3tpvOT9nzw1G3mfwWSIxIfc2FebNmweO4xRnH/nD1tTghL/NNxnm7JuDPcfjm8uwraQNXQNeTJ2QoeuZWKxaGH1FQUMPBn0BfGXuFEfyo4RUbiIrE/L8x2L/Q2QFLrZE5CFZu2t70dNctfRNUsAQ6VtePAgAqq4S5zsfnGrEb94tQMmD5kLYOyk7nOxvy+mNwtFjPN3brHhX8HKzrbQDbcWtuHaxvSHd46nKjNTI1uJW/PsbJ1Dx8PWO5UdMMqt4nmTtr2ilR4WxY8di3LhxGDt2bNQ1b0A9hKSw0GNBw8dLlkZLn/TdFw7gRy8fifl71eRGL5Vt/chbsRGtogNNzRHv2ozN+51sKkO+ADr6tSc4rGKH3BDJydaiNgDAgMdclC67ZYfZnmxqylr9WjJGfmS5t8XqK6xMnvFy818bSnDnG9GuXK8frENhY4+V7DmGmfGR0gD9rZG9PsOyQ5aTURadhuM4vLC7CoNBd1L2V2T0mERrZkfeVOxqPDGNXmUgy8KKgoOW2mhTP2pVuassfALz6QZ7OpxYz8aMJve2f/7LIXzhkR0OvuH8RiybyTZreF5BVaMMQwFp7ukxUJ7xKvr7Py4WDh62glJf197nQb/HWjhrI0MiM+WoZlSequ/GO0f1B0cYDfR7A3hiazlWvH8m3lkxBRk9JonlDEC85+r1cD6Fqv2Pv5/AuuMNMXqbtXIdja4km860IG/FRvRZ7Cz1UtLSF5P3EOYmdara+/F/XjoEXyD5I2UmYnPlbPJv4/vM0aST7J6EbOoZxux7N6KxW7oHTv6Wxu4hdI8EvBCPRTYWtmDFhkJb86SHNw6fZf6uNUq68o87ceNz+23Ni6oxaWHY5mfol++9eNDU4D8ySWw+P/GCz7vTLp1OYdjo6e/vx/Lly3HttdciJycHLpcLK1euVH3F1Gp/AAAgAElEQVSG4zh8/etfh8vlwl133WU2rzFnaGgIg4ODGBoKK6DvvXgAt7121FAaVnQia9YzXns0tGZg7cpXWWsf/ry9gv0Oi2nbxaYzrfjteuWORS43SsTknB4d97xlIIxnIrC9JOwK1G0iylUsae/zoKp9QPKbmj7QKzejFpMN4vldVThadw4tvcO6n0nCsYYqdsuO5MBYW1KMJlH0uR3Y9S37KzvAccC+ynD0LKVu92uP78Y3ntgd9fsv3zqJd47pn5Dj5cYqv/+wyPSz9TqCnKhhh+EQiTulXJOffzj2q/2JcKbQlqLwJKM8qmQoFEzK/spwIIOuri6sXr0a+fn5WLZsGdasWaP5zAsvvICqqipTGYwnlZWV8Pv9SEtLQ35+Pk7V63c1SuLgbZKB2Ymz59Cnw8/crihht792DC29HvzmmkusJRRHxHITb/QYo/d94NwytZOzumbTbu314INTTfjFVXPtzZCMLz+2C8EQp3sDv1zfjDY8/iAy0txRv4t1hhX3NiPykKh62ezX2yU7gh530CzU3NOThBapHSs+P/zrIRypPQdAFCZcJVk9/bIWvNzYQW3nIAa9ASy5KDvqmtyYODfow+8/Mm8oSdK2wb0t1quPRl8Xzyaxuywckrq934MLxo4Rfh8aHEJpaWnS9VeGV3pyc3PR3d2NvXv34tFHH9W8v66uDvfeey9eeOEFUxlMVLQV8+hYyv/+Xw7h9teOad6npPSLmnpt6RBCSbqUqorKJ5np+LcVt2LHyCpI5BXxWRp08nVW0/7t+gI8vqUsatOq3fDL/71DsXHD06K6YwAHRecv9A77bXcJU2ulz+6sNP2sGkbkgTYmG4fX3xS9zW6kssgbPDxvHalHUXOvZipOuJabSfGbT+7BTc9LXdX4SQx5nb9x6Cw2FrboTruyrR9XPrIDA179hh5r3KE1qcLSD4k4ceckv/uQPQk6WnSn4ZUeozNxd955J6655hp873vfM/qquDN58mThxFmjODVblYBtBAB7paeqfQA3Pb8fDy1bgn/7Uq6udJSKbc59m0TvStRSCCOVm9gdpslH3xGvLMTy0FgxSit/Hn8Qbx4+i59+bbYjm9b1JOkPOrv3o6ZjAHNyIid55z+4DYtnTNB8zoq+0cO3ntoLICIf+Q9sw1ULcrD29isdeZ+cQR0DllgFaknU7tvs19slO7EoFyMHWiZ6YAteXO2W2q5BH57YWm5zqtHwcgO0ad5rJ0Z18NtHG9De70V5az8+nztJcs1OEZGPLRwbxyWitTPCm4fZ7u5CWYxkPW1MGnJychzrr5zC0XN61qxZg6NHj6KkpMTJ1zjGzJkzLafh1ADdTGNcd7wBVy+6EJNES5Sq7zDQBbIG1z1DYR9QPQcTjiakclOgeF+iG29GGPQGkP/ANqz7+ZfxD7MinZJct7+0txrP7KjE0ouy8cU5ky290/zKwMjsowPlf7qhB8teOICX/vXzkt+Lm7WDIdihb4yyp9ze07TVNAarn/+sogNjUu2Jp6NWm2rXeoZ8+MNHxXj8+5chc4x2B37z8/vhcgEf3/U1w3l0CrtkJ5GO1+K45HF1UxvDmvkG+QpsMMTBHwwhzR3dVqxMaEXkRupqpjdFs282avSo6Wp52auVh1Jd8L8n6+Z8J1Eq+8yMDOTm6pvMTiQcM3qamppwzz334E9/+hNmzJhh+Pni4mLk5uZiwoTIDKnX60VZWRkAYNKkSZg1a5bkmcrKSmFTldzHsLOzE01NTQCAWbNmYdKkyMAsGAyiqCjc6MePH485c+ZInq2trUVfn/KgpaAgPLCdMWMGcnJyAESUQWdHJwoKCpiWfUNDA86dCy9pL1iwABkZkYNABwYG0NoSXv4N33MhgMgMgcfjQUFBAXPfSEtLC9rbwyGP586di3HjxmHYF8Rv1xfi6oU5+NU/pAMALrjgAlx88cWSZysqKtDXF72kLlYWBQUFyM3NxcSJE4XfAoHwLO7QMNvAqampQX9/+ITkJUuWSGYHBgbCm71bWlsRDEUrQ758hbyIlFp9fT26u7sBAAsXLkR6ejrz+QsvvBDTprEPXisrK8PChQslvzU3N6OjIzwgnDdvHjMWfUFBASZPnhw14CgvL4fH42HOgLS3t6NlpF7FIlHV3o+rn/4ML39nGqaOTcW5c/6oe6qrq4WyWrp0KVJSIh1gV1eX5N+TJ0+WPN/dfQ4FBQUYN24c5s6dC48/iJZeD2ZPkX6Xz+fDmDERo7i3txd1dXUAgOnTp2Pq1KnMcmgZciEQ4vDe8Ub8w6xJQg3Vna1DQagd8+fPR1ZWFrwjnfnA0LBQrzk5OVE6oqysDF6vF6mpqVi8eLHk2rBneOSeUky+7BKJjvD7A0K6SjpicFAaXIBHTUeIqampidIRfDkcagjL/9ku9ubgAca7CwsLwXEcMjMzcckl0r1sWjqCp6WlBdOnT5c8W1JSIuzzuPTSSyXXeBnk0xk3LrIy5fF4UF4enmVW0hHDw8NwuVy47LLLJNeGR/QSgCgdEeJCwrUJEyZgOH0yfvzqUdywNNwuu3t64PWGz0OSr1p0d3ejvj48A3nRRRdhypTIgcP8akBZWSkCF2Zj/vz5kjzV19ejvy+se7w+6XlLfX19eHpjAT4u6MNXLs7A//3aIsn14uJiBAIBpKenCzriTFNYP6rpiKGhIVRWht35tHTEkiVLIt8CaVuW4/P5UFpaCgDIzs5GXl6e5LqWjmhsDK88z5w5U9ARABAKhXDmzBmcPas8QeXxeFFQUIBFixYZ0hFFRUUIBoNoGop2dWpsbBS+l9cRfH0ODg2iproagHEd0draira28OrF7NmzHRtHZGeH5ZsDN7JiEqampgaHq7sk3yseR8jz29Ojvl/46qd2o98bwrafzI/SEcFgMKqP5NGrI+TIRytKOoLVXwMRHdHcHH6/uM47OjrQ3NrOfC4QCKC4uBhAWEfMnj1bcr25uQmpPWE9EEqVyhmvI87Ws2W4oKAAQYXzFYeHw30KK1iBuF5bW1uZ44iCggKJjojkl60j+OIYGBhQHUcoIR5HyLGqI+TwdRcKhfX3gI9d53V1dejtDetGszoiIyMDCxYskFxj6QgeM0EUHAtZ/fOf/xz5+fm44447TD0fCASiDAWO4+D3++H3+4VBtvwZ/rqcUCgkXAsxGqqedJXgnxU3Dl5xB0fey7KWg8Gg8Kz8W0OhkKBQgqEQntlRIYlnLy4LtXT5b+XfP+ANMPMr/lat/TOsMhSeEX2HOBW1uuFnV0KM/PDvEyMuS3G6SkvGSt+qlD6gXjfi5x7YVocrHt4e9bvf74fPFx1djE9XzmcV4b0WJW3DI+9UllEl+Wb9my8rTiT/APCrt0/hm0/uYX6XGLGcKZWhtN1IyyoYCErKUDBXNdJV+1Y+Lb9fn44QzyoqyXdTzzDWHmlS1RHiNFj4/X7FTpUnxJjh9Pv9+O7bjXj5aPRAQC6H4lVTcR6NlqH4fvm3atW5WlsWP6uWbiAQEPzz2/vChggXCilOmWvpbwAI+AOSuvEGglh6/1acbOhDaKQ9seQlOFInav2CUR2hVYZKOoJDOCqSGmbbjZ4+UE1PcuA065z1vM/nY/atHKfVBxrTEQ3nhoS+RG/dGBlHBIIh/GlHLc4NeIUyVOopA4EAajoHo34T50k8kSivD/mKRL83JKQhh68XrX5BrQy1UGrLSgXAfytL3wWDQfgU5EyrbsT1ysqj3+9HQHUcwc6wXncztT7QzDiC/155ul0DXvzthPIqvNI4Qp4fMzoiKo8jf7ugLi9qdaNXR5jRs0ZxZKVn/fr12LJlC/bv3y9Yfjw+nw89PT0YO3asanSr1NTUKH9el8slPJOaGp311NRUxTRTUlKEa2LLlsdsuuJnWTP7/HvDqxMcfIGQ4M7hdruFZ+XfmpKSAvdIPis6PFh7rA6D3gCWX7dQuD8tLY2ZL3G6/LeKZUMtv6mpqXClqC9ap6WlRZfhyCMpCuvHqnUz8kyK2w0XooVeS06UylD8vJrfqVYZqqW7vSLaFzotLU3Rv16cLgv+ekoKuxzU5Jv1b8HtcEQO+eePyjbNKiFuc0plmJaWhlQ/u4zcqeHviSpDjXTT0tIQCoWY7ZGXFz064mR9N2558aBwPTU1FSkp0TPOv37nFI7VdeNb//cipLhcTB0hToNFWloa3KnqAwiXiu7ZWN6PJ2TXxPKys6wTd71biE9/9TUsuShbkkelMhT/LU+XR/6tWnXOtzlWuxA/G12G0rqRR7h0paQo+p9o6W8AcKemSuqma8CHfm8AH5Z0I8XFPxMtL+4RlyGlfkH8TZL3qegIrTKU6wjx4ykp6i52Wula6QPdbmX5TVEoB61vHTNmDILBINJGdIT4W9XKsKnHg4ruEBZPTdfUER5/EP/4p9341T/Nw39fu0B33Rjp7wsae/He6XYcrUvDI9/KYepZcRpq6bL6ezFKYzlWui6w60WerpqO4Gnt9eDRzaUIyIwVRR2hMFTgv9Xt9kZdc7vd4BTm2zXrxp0Kpe6Tl+9UBRmO6Cz9AQ5aej1oEQ1h1fpAIzpCfJg7a3zy4Kcl+KhQOYiF1jjCio5Qgs9rqsKkk1qedOsIE3rWKI4YPUVFRQgEAvjSl74Ude3ll1/Gyy+/jA8++ADLli1TTGPx4sVRFZCenq4aGk/u1iBmypQpEpcIMW63m5lueXk5/H5RGNC3I5vSxUpJLU9TpkxBfv5i+EeefWp7Oe69PuxCcfHFF0e5jvCMGzcO06ZPBwr7kDWyJBoQzVBnZmaI3lsreXb69OlRy9g8KSkpqvm95JJLkH2oF2jyKN7Det7tDotSVlYWcC66sbLcgXjGjw8vm0+fNg3u+ugzBuRlL2bWrFmYNWsWPjjViEfWnsR7//5lXfkVI1+SBsKuilpumWr5UlIAU6dODS/tvt0oqN5+jx8Pfhre9zYrNxf5+TNwtLcGQJtEPc+dqxxiWeyqIv638NsFF0jKQcmnWrwkDYSXx7XKLz8/H+mtfQCi6y43Nw/5S6NlMTMjA/nzlNNl1QlPRmamcM+ECeMk19LSUiX53XOoTnJ9/vz5GD++C2jzSsrWHwz/7/L8fE1FqiTL+fn5aE5pAfYrG5RiFxGeyy67DHirARzHoaioCGlpacISv1hH7N8dDvv/4CclePX2L0jSYrV3uUubGPH98jxlZGRo6ggl1J51uVzIz4+4w3XVSctpYnY2MjJ8QN9AVMc4adIkRXdDvrYWLlwoCSDBk5mZBaSmAy0epKdL5XvChAlhPVvQh4kTo9OXuyGJUdMRWVlZqmUod+EQ9ydTpijvdRszZoy+vorB5MmTmboBiPQLZ9EMHDwnGcvyeVN6t5aO4N33xrSEdYT4W2fOnBnl1sO/+4YXw2fiKYV8F+uI3uHwQLewMdz3TJs2TdGd2co4AgDqevxYfcaP178wSVhZ4iAdzIV1RNjFiFcnclctMWI3UACoaOtn3sdqe5Lxi6w/UtIRfJAIt9stmd1ftbsSH51ujnqHko5I2dACIHrmns9n4VAdcLxHomtzcnIwcdIkANEuwKmpqZiz4FL0ewKYMTEz6vqMi2Ygf2TP6K4y6YQjryMaXS3AgWgdnJ+fj7SP2wFvtAdGZmYmALbbsxglmVKSJ61xxPjx45jPBmTeCPI+STyOkKPUTnn0jiN4+PaakuJCfn5+eK/2+80YHByU9FdyNzoxenUEC5aO4MnKyhK2TejFEaPntttuw1VXXRX1+ze/+U0sW7YMd999t+pHJgoej0dzyV8L+fJbY7eBA/QYY69EDfrBRaYuoq5p2eJGv4m1UfG36wqjFEW80Cs3fIfZ0R89G2Y38mqxO4KZvE60JmCs1JSRjbvM1QiV5+3aPG3m+ziEZYeXm08KmjE9OwNX5F0gue9o3Tn8eXsFfn+TslETL6xEJRI/+qctZZYDHCST/rSKHX2VmGQJIBAvmnv09+Nm2FzU6ljajd1D+Nrju/HmT7+I8SNyw6PkqaGE9skd/Kq6/ob3z385hPK2ft3nmyUlWsXBuH7/R0W4ful0fMliACAj/Oz1Y9hRyrtdS2s7FApJ+qtkwZTRs3nzZgwODgoWVklJCdavXw8AuOGGG5CXl6do9V100UVMgygRcbvdim5KeiM/Ge1jNxa24OpLpyI91ZkwgEZ0muTQQI17xX6fStfsglX2au9QOhTRKdTkRo7TZ7go9TX8yobT73Ny7KT2BT9dewzzLxyPiy+Ini0Uno/jCNg3YnTuq+zAD66IrPampKQIcvOrt08BYM90t/d78V/vnY5BTu3DSGm/uKfasXzIGQ3nTxjROYRZ2HsyFC5p4qTU9Xv8GJ+RJtkHzHO2K7wv8EhtF749wy0ZtBo1epygnLHKZegA0vh/giO8fugs3j/ZhDMPfDtm74wYPNG4RtzAk03nmDJ6fvGLX+Ds2bPC/9etW4d169YBCEcoUVvmSiasrEYpDqhUGm9t5yB++dZJ/MdVc4W9O9GPmxuoOT28szJ+dFpJxXoFSCo3ZxXvAwC/wmZYI2Xi8Qex4STbzS7eYbH5t7f3e2yfZRenJ097Z1k7dpa149FblkY9p1a2sSqtc4NhF4u/H6kXjJ6UlBR87nOf0/X8JwXRLijnLbK9QSxG2wpPS+8wpk3IEFYy7facEBuCQjAUW9/gDPEa8BoJqWw3rX3RruhLV27Dmh9fgZ/97bjqs4LcvLcRQPwNhj3lyoNsO4j39yUzwh7MEXkeP3687v4qkTDlP1BXVweO45h/1AwejuOwatUqs3mNG9tL2lDdoe3vyYKl8PJWbMRf90bPZHr84RmXbh2z/7GYnTSirHmlz1Iqet3bnOocEvkgMC30ZH31ZzX43w+KmNfidTipnCsf2Ykv/nFnzDsdtZgc8ZKKQDCEACtKjsUMdQ54kbdiI47V6QtSEWuiVgFldeNUfUiMY9Z1Fd1lhEc2lmBHifOHPLb1efDlR3fhraPsQwSTnWQcmJppu3Z+52Oby6KCD5xuUA+DzUIrcqtRZOdZAgDeOVqP946zJ+lue+2YgbTNFGBiCFc8JyM9/iC6B6P3NRklMUrSOI6FrB5N3PG347j2z59JftOr5JSE+4WRTclqsBq1/L3t/coBB6Rp6Yd/R5MRv2XGZ9rVEVjdf5K8Jo8+nt5eIfl/3oqNKBk5DFNwO3RYQ8lngbSI1cqg0eguThvIHMfhuy8cQFFT9LlfVjtC/mygbcXW9gNsOtOCvBUb0SdzjRnwBlDVbm7yJ4z8+4z7+xvB6KDIajZe3lerObPOfi+HXWX6Z7i7Rw59LmpSju6kh6KmXixduVUIHc7nBYiV4cEucFPvtkmEvIGgYrmalY9YlOVLe6ux24aDhu12imB9+/snm8ynJ/q3lr6U15c/GIJX4UgBY+MjDq/sr8WQj310gROI26hVfrj6MP7hoe3aN8pIViNHDhk9OjF7Uq+d/TkrrSsf2anvWfuyoZr+qXrjs0u8YlTqHFZsOKP9/gRazeFXPfXdK3fTsuc7NhfxB6DGp1zivbLEo+ajrrUC4BTFzeyDjj3+EF7dX8u8pgc+xL1Vd86tI0aTfDbwp2uP4eqn95pO1ylRdAnGk548MMLVxllWtxa3CXu8Ysmbh8+i3xOQnP3Egi8yfi+IVRJ5JefhT0tx0/P7FQfHcjjZ3/EkkfrAWCL+6lCIw7CPXXc3Pbcf/R7rxkNRUx8e+rQEz+6sNJ1GPKuqQLYCeKaxV5e79K2vHXUqSzGFjB4V1E691YsvEGIuGavJvJLbx7vHGuD1x75zBKDZU7EasVbn1t7vwcbCFk33NnloykTGGwhi9r2b8OK2M2hv1zt7q+IPblN3GjdfdweUu3i3gfCbwvex3NuE1R9G3gZ9QfR5/I4HmIjkRfr/Bz8tMSA3UtzCgcjRH2bEPVdwSZElc4YxA/7rd07hmR2RlUazUev08pc91Tiu6L5ndr9jfAeLvcNS41Lv6uTbRxvQNeBFY/cQTlbUo6WlhSk7R2q6mIYN704tDvLCerddbTiRjR0ePlS01jdH9dEJaHAoyTWfVW8gZMsYR2dmNPOlRO+QH/urOqN+Z01WPPBJMf57XQEzHVaABEb2NOFdk50ci8VSJ928ar8QNEeNhnNhzx8+Z16fV1HnJDKOhKweLbS0tCiePisWST7mvThKGH993YlG2yKiDPuDeHGPtlucXVjNtVY/8O9vnMCp+h68cusVFt8UTVW7sdjtduENhBXhtpI2fG2atABYHWND9xAmZDjTDHeUtJlyt5Hz0KclmDkpE7d/VfmcCb04NauuJGustqeWg++s2i/MaJsJmcrqnI3S0tISPoPBIO4RC0++0lPa0ofrn91nOV9uRll+yDjTQwnNPT06+vnHt5QBMFc3gLHJpnhhZAB94mw37nzjBADg3e9PxVDQHSU7P1x9GGPcKah45HrJ77yuSk8VH7Kp792Lfr8FSy6agHU//wrzeijEoWPAiwsnZERd0zQoTOgIYV+W4SeNvMNenF5h1Crn1Z/V4MqJQ5g4JnKj3YNtPS76anj8Qdzxt+NMt1pWnW/SGeqbH7PFC7OlnEimtdfrRVNTE9LS0kz1V/GCVnpsoqS5Dwt/v4U5C/nB6YgPq1XlzPt2mm2vjg061Zqjwit59xmxexszEIKOj5W//bMK64PPWPCnkUGcEmZdSlwIh0O2g1f21+KBT0psSSvWpKhEMnhxb1VkVWSkJ7biwuMNBPH3I/HbXM4bPUFZOPI2RnQnNZRastUxgpKOcGroEVnQi/daTmx468wAbv+wBQcZhjfLfY43epgTA6KfWKU37A/iWF23Yl6e3VmJL/5xp243sWRFKWL1FQ/r3zPh8QexYkOhfZnSQFy3XcPS+km0Bav8B7bhqEZgFukEtL50Y3m0ApFYkNGjQl5eHubNm6frXn5ZnLkJkrXJn5GG1kyo0nN6cH6DttrFsCvbL948IekEeWNG/KwTRplTn650ajYQPilYHsmQz8fO0jbm7yye2FpuKm+snQtO4kTqXQPe8OnP8ncZeJla9La/7q1R3UC+sdCY24cZOWO5HekJ+c8qA6WVHrvg0+c4Di/srhLCbuvlveONaOyOfC8rspMZjAbRED+jl2BI/z49u1mxoRCHqrs076vuD3fnP1pzBEDYV7+1V9ngVZMTq3r4xNmwQaS2F/btow14zsK+iERCLhqdA/rbxp7ydrxzrEHXvSfrlQ1NM0yfNl0yxrFLwvNWbMRfRGdtmZ124A1zFmwZ1bmX1lRu7CMR3SGNkpWZhXnz5iXdETVk9KiQnZ2NiRMnMq9966k9ptK02pnEoq3wrzAyMNDK1iv7a7G5qBUFDdYiDgH6yiAWK9d1nYOK11JTU5GdnR31e0e/Fz99PeJyxnGxUcCxWsnX6tzEs+9afP7hHbj8QeUZU+Y+Mln70prFDjJCR/P88q2TitcCKpGAwvnQB2twxJIbOSxXszQ3v6dH+k3yldJ3jtardrpKeeeNnuZeD57YWo6HPjW++veTtZGQtPJ8mRkYtfV5sP4EO/wtz9biyCSD3vD4DeeGJO177n2b8NxO512LOY5RX8ca8B9/P6H5rDtV6iZ786r9uEZH4Il4roN9eMp8JC8W8XRZ0sMnBc3oHQ67zIdGhLCxW3+U1FtePKj7Xnmtstr82HFjJWMco4NxtfL+y54qUxMSZt8nR/3spNjK/HvHG/CHj9jHSiQbfNmlpaVi4sSJuvqrRIKMHpO09XmZvwvRXBQ27ln3PTbXWK12BpaeFrtKiApGb5qWFVQCTarojdJkd33FayjgxIBK6YwHFsxABjbk4cevHsWC322xISVzsPcqsVd65O1nxftnVDf1ar2TD8xiZkWpb9jeMK96VkDM8I9/2o2rntwjCZf/aaG5A2HzVmzE/SMDHn8wZOocJbPRQ/ttCHVr9/hQ6jqnft0pBrwB/M/6wqhIX3o/taLNeOh2jz+IX719Cve+XyjkAQCe3xWbfbp66lFlDsjU+1hVaWf4ZbNYEWkzzy5fX4i/HTpry/sJa5DRYwPh2Tnl66z+SnVDrexv+buUrqlhxnDQuypV0daP3zIipmi+U5b86YYeIaKQ6mMstz8btEjXgBedA2xj1g5iObkUb6VqduCy5P6t+OOmUhvzwVrpsT6qOujQYJtHa2Cgrm+0a98fMC4hEfc2w49G3ssw+q2kp2ZUs4wyoweRvrg7+hBpM7w+MuB5fmclfvDSIcV9Vkr5UiojiSzbqGASfMEkCqOfvv54A9493iCEZzf9XhOaVu4WmkiuTnZOUrH00P7KTpS16ptw+bdXjhh+ZyzOiSOSGzJ6VPD5fPD5rJ9ca1SpOdkenejMfvdBkeYgUI8BtaO0He39zhkdWnz+4R244uEduu9XGzxzIY4pOyxZiIUCtqvetxa3oplxaK2Vw0k7RHU+4A1g9Wc1+tJg/HbvB2fwf146FMmXvuzYwos6DhzWg8/nw+8/VHeFcMuWsEqa+/CJgZUItcGNsNdO9ju/0hNQmQ7Wqn/xSqcwuSOSHTvr6ynRfjh5u9Mrp3oPf9ZLw4grk9JZIkroMWT13MMingPAeA34zbzVbFb5fSm8nDu05S4KeX5Zr/X5ApJ+6oKx6ba9f9AXFFY3+HcXNuk/x29fpbVgRGr1Jdd/dhzsaoTI5HWSzS6I2FHaDq/Xa8sYOZaQ0aNCaWkpCgujo6qorUY4rcPNpF/TMYC1B+oMvMPYS1IUpEhrRt1sczdaBt5gED946aChs0r0cIdKOOj+gX6UlkpXLBTPTXDAzB3yBYXZZTv59zdO4EcvH1a83qZhtMrr/KPTTfjCIzs0D0jUSzDEaUb7YWFHDTxnk5tKaWmp5oqjfE/PDc/tMxT0QtyG9KyuAvYESmCt9EjyZTrl6GdrRHtyhO81+IJAUN8DrLPY7ERP8sND9rQhOU5+GdO9zUJ6Zp89UNWJLlGbM3vQLbK1ncgAACAASURBVIvbRg515A8lPt3Qg7JW9gHFTsLK79mzdZIxzj/MYu9hNktJi/Q7rY6Plr1wQPUgTb3J00qPecRFt+3QqahxTqJDRo8Jbn/tmPZNkn08ETadiSyne/xB/NNTe1Ayogz17PcxM0D+8atH8dT2Cu0bTb5LPussPM9a1RD9W3WlxIJWkncodZ1DOFbXjZf2sF1V1N4VCnE43aB/diqSps77dNzz9yNn8bLO1Q+eV/bXGrpfiYPV0bNtalG7PqswNmN2pjEc2CKWK3xiqfukwNrBfHcqGL6O96k6R3e9w37cxtBX4vzVdSkH5JC8UpipVv46LQPKLzIi7N7kLEesXvigE5vOhOtb774CsYGnlM11xxsw575NpvKolxDHoaipF7e+etTWfRfxQLLflVGoRoxqjz9oyx6R/7fmSDjIhgFZ5Dh9stszctAxH4TAFwjhumf22T7H/4Ksf9PTf8d67G/H5MAaA33b/P/dhD+bGPs4jVbdkFHmHGT0qJCdnY1JkyZF/X6oRt2VKxAM4ft/ibjYKAlwY/cwajoGsWa//gGtkJYBfyUjm2C9gSBzqdenEjpSz+Gr/C1Ha89ZntVXe92usjZc98w+HKk5F3X/uhONTGNATcG8cfgslr1wAJUGN36npUVHb9PbScr53w+K8IjCPhe1kLRizCyjnxv04UcvG/erTiY2nrFm9GwradO+SQO50S2Xm7wVG/HaAancqk6MiJIrbGQb7GYmFfS4ZIjLo63PgxNnpatudrsz6U2O14H7q8K6Wy0Urhg1Vz6eVQbcGs2G6eY44JGNpdhb0YFndrAHcfLobbrTZvymNCEVCIbw/9Yor/QO+QJ44JNi1f5CnDTLgOZXRPSw7IUDWHL/VslvHMcZdh8EwlEJhTQYpSKXXbPuhDxm9xYquVwWaEzOsXI7duxY5hjHbviisnVBVEfx+YMcnt8VHRbdDjWUbPvenGDChGyK3jaayMvLw9y5czXvW3+yUVCAHIDukZkdvWgNSKWR4IxjpG1+dCqydCzO14Mq4WmVVnpYPL29AlfrCaM68qHBEBdVnmoKq2nEZ76lN7LvRJy7NfvCBqZ4dlCtTOtHDDQ+zKheWOf0KMEOvayPLz26U9d9ZhS0fOByWNXYN/YCO/o+sx2XU4EwzCIfCLDk5i+yWVyrwRjUBh/CwFyhUPSuAN/8/H7J5I8erHyV2oGD/CU3o8dTCw4jdm+LxRhHaV9TkIscsSre6yC+NyPd+n6Mu985zchU5J/nBn04UKWsB9452oDXDtQJLqZOn8HGb4oXV/26E41Y9IctqjqbddyAUR1g1wDeaFteseGMqfewvm/69OmSMc6nBs8mM4pVQ1ECIym9kypWXMpHq63zg5cOSsZNerj44ovpnJ7zkeXrCzXPimDx0t7IQOZkfTdufG6/5DqvCx0K0MMkKHqBbvc2g0pb2NjJv4elvEb+Nrw5XGETtpAuB7x5+Cx+/c4p4Tc7FLGecLZXPbknyscZJld/7ELtAE55/YvPWNGL1redEmYnTaw8mO64Eqvb0tNRmx1g2TnQ5Mu7sFHfWVtaLot83oTtNpxzJ8boOZ+HdUm80hNPj5MQxwkyIJ5jkuTJxqlnpZTkA/QVGwqjDHIxWmXW2D2MvBUbLUfNFLehA1Vho7BPwejZW9Ghud9R156eOEmE1r44ARPZU9svYwdOl1gs9vTY8g28Pop7nNUIx+q68faRes37rE7CxxsyemxiwBtZTtfb9/CGkssFHNe5+dpMI9E7k7S7rB2nDJz4HAxxeG5npeYqiJWBV63O/QaRd6nT2ufB7z4swo7SduE3O4yOu946pX0TdLgg6MjLqfpuwwaIUrmoHcApR6+v/X4DUXf4k9udItGUspqBr36f9Afr41vxCoa+xPg8LV8fHdwl0VGSg+qOAWwuUjb89QYy0M1IUT+3sxJ3MdqeashqRlZaxTOzNs6ecJJ/R+/D4nnnWAMe31Jm+X2l8skgk3DQ1lNnFfsUTrF//eFfD2GvbL+i1eLWWlFVQu8eU/lkHv9t8Zhki7zbxpcz2oqaW6U0P/bT2uvBba8d1R0YRo1k2dOTLPkUQ0aPTYjbX7/H+MZKtYEHJ+2Bot5nF7evPWbo4McjNV14ensFjisMXIUZXAUVI2xkZj1rsjVpbY5mDSrkncMHpxoF5Sm4viTQ4sD9HxdjV1m79o0i7Dibht8XoVUz//rKEeV9ZIr5sJa/RJoxA9juM0roixQl/b+efXSAcnHrsV+dir4YST86Hb1p9g774Q+GFA+BjoJjy+71z+5DUVOf4rvF99upAj441cR0JdITZldcL7//qNhyXli61q5WGquQ1PxbdpW1C6vXSiv44m+o7RzE8vXhM+bEB+fKnzxSew4vyla0jHgIMPfWmRQoM+MLQFm2ipr0rdxaQc9Kq/FEo38a0rmXywm5XHuwDnvKOzQnNoFI1o1OCIvzXd81JPn96e0V6BmyFj66Rke/xcmmRJINMnpUqKqqwpZD+mY1xeODRzYq739hPqv4uysq7UTiR2vUN7lrBSzgv0+18zDYpiIuM+zZST1F+Zt3C/DyPmPR0uQMDg6iulrfwYZGB+zCOSoODij8wVBU56pkyLCCPCjJbCKIcizaU5Qbowry+mfJjbyN6A1kYO0e9ZvMSp/HH8Tqz6ojAyETaeQ/sA3z/3ez7vv5d2yXBZ7QmhkWl0G8u3e1vUcAMOyxdqaQOOiEYvs12Hj0rWJah5WmHh3+7M5KYaJPfIaU3S6n31l1QP/NNqFn4q+xsQmv7DS3R8gMtu7p0SDW7VVtEleJ/VWduPzBbabe9/Undgv/rmofwHM7K/H4lnIEgiH893sFigcgq6FnT5c4SEh1Ta3ucU6iQEaPCutPt+HnHzXoulfcFQx6jS1vulz6B2Lx7niN8PqhOgBhQ8TwDKHG9UAwhL/urY7yb9Za6WF1VCxF3OcxFrggKn+BIAYGtM8F4sAZGgTsKmsTZpLM7PPoHfbrUob3rCvAtX/+jHlNXpfX/PmzqNkttc3OLE7VdxsODW6m/yxo6Ika+MYb+Xew5IaD1JCyarhZid5mlZc/q8EfN5XhSG2XJGEFDy7dBEMcBhXCFyeKG4YVV19O9recUNCaW017H3tfjbjsDMSsMYWd7q4HlXSQTbMedk06OSWaSumKsz08PAwErfV10ekrf1Gso7cp4USZq+1Rjnq/6J4eA4GvlCYd+ORCIQ7lbf3YcLIRz+yIjlpnB2KX+KHBIV3jnETCXIzL84TGPuPLyByn7BeshAsuiTDL5VrcQMzMlMRrpYjPake/FxdOiI4spGagREJzR19be7AOuZOz8OjmMlwwdgy+kHdBJE3580qJsN6lSmwLUanOnt0ZCexgptO9/pnPJKFZldha3Kp4jfXWbtmyutz/PSoNjpPk/+GNsTng7Ggte+9cornHyekZ8suCTuh0b1P4PZ5fy8+oC7rMJgV17/tnUNjYi7rHboy6xtKb//UeI1KZAfzBENLcKbYaVC4XFCuHby9Ohf1WHCSL/q1ltKn1XazAPHLufd/cfjFW+/VbONCIT6170IcOhSALIU76fbvLDbocm8ybXuRiwv+/XuaBkWqzJcsybLRc3a2g1RxYl/uG/Vh/vBG3fzXPFtdvQDyecU67KqUt/gI+mq5TBybz7sBAck3C89BKjwqTJ0/Wfa/Yx16PzMtdh4w2u9MNPTHxxbUCXw4bTqrvEzKqJNYerMMDn4RdCAMhDn8UnWHDWmLW0mlOLLlnZ0/A0qVLbU+XFYZX13MjD+oxeMyQOcZt+JlEmX03yq4y7ZUipW9jdfpy+dMjN3r7aaVziFiD0fDvHPaMGKxOVA8nejdrAG1lRVgtqhyrPt4/2WTwbVKMBhPp6Pfq0IUqwQxG/lYapGWNHWsoP2oo1oNGBUWVMxcefHWJDAdWXQhuyWaFjvFc0EQQCvn7//mlg4or3vJ+a1+F/gAuANDHjwFirAfv+yDizjZnzhzkXnyRremr9ad26PyChh7d59PxyD1Cvvb4bjz4aYnhvbFixN9S2NgjjAHFn7irrA0v7JZOVN79zimUttoTuIMFb8QGY9DBLlq0yJFxjpOQ0aOCkRkAK2GlDbm3idK+6fn9yjcmAOJvkm8CFcP0+9bZE7hk7+E3oxoxpJxSDSkp2s3LiruLk/7RakmzcpyRyjZ61HJoVSlvGhnQ/+rtU3hV5yndejZqavGTtcc17zEyoxkVpCAlRfN5vVLzd4UQpErpf1bZiXOD7M2w8jZl90y13eLMKfzbLvYpRClU0j0Hq6PvH/YFsbVYakQrGsz8ioyO2V6riPs+8SqumUnxZ3dW4vMP7xAi4amlYadOU4ripucT+GxUdyjrC7sm0p1zb+NU/w+E69moKzLPgDcgOe+O546/KetHtX7ZSJ999zv6oqUC4fpWOlJCSdfpQeyO/Z1VBwS5EsvwT9YexxNby4X/+4IhfHS6GffLApAEQxy6B31o6glHYzS7IsaBE4wvI4fSm8WV4tI1zkkkyL3NAYxvTDeStnEkG/lj6OumpcMiG/Lte+cjm4y7SXEqXhCRiEk60zK41K7UMRnpmPVgOEqMyrUQB1MnnsvTN7IRncXzu6rwjUtyDJ0t8fZRBSNA4YP/4+8nzGTNEFbbtJ0vtRr9h+eIykG2fN5b+NnaGAQLiFUUMQB4YXcV7vqn+VG/s3Tvo5tLdc82O/UFPUN+TMhU3ldQIxr4a+t06f85cDhUHZYFfjB4ql55756NCz1Mo+fJreVYpfPstz0a7mpyV/ZECzik5N4m55DqodPKPKxwYPmecoZr88jL7RqH+/SeVTSC3+7Q82AElzEwnpH3+3Pv2yT8m+Wea4TUESMkFkZPMnprJJeJFmOMdJTiQaUZQRC7xwVD4Zjv7JPjlRNPdHc3JfZVRitJvWVoR0ej10j905Yy3PT8PusvFL+bM2i8WFhRNIRK2gPeABb9YYve2yXYPTB4enuFvQnK2HRGeW+TXZgZkKuGuNdRGxL3T53vZHguKfLD1Yc103v1gL7VOTvQU8QvMFajzTSx3aJB379olENZi/7Ih1pyUqDz0Fg5N6/aj889tN0WfdI1IDWajabJur+5R/uUeNZzrEM8xQeCqyeo3Z/Kx5QJZvPowmiVewNB5K3YiE8Lm00F+7GrzxKX9Z93sPsA/l0hTlmGXC4X87wso3kIp8W/T/sjG85py7QSw75wHYgpbo64y/ELL7FwbyOjZ5ThMRAC9LQoDr/xJXqXpKN7+2g9vvToTsOWujcgnX0vae6T+FIbxapA6338nWP6IuQZereBvP/izZO6fIRf3FMt2cTHfnH4L7/Ph6X3b4m6/OEpa/sIxCitWtiB0Zm0WM6kizlYbW6W0mmMFIf81q4u7W+yuvdY8QwTlb2Juk+Ct4BT58DoMQSVztdYoxH6WJ62+Bu0ZtGN9BVGZMpoXcn7GrPixVpF4ctH3j+xYJWHmdC7gLmZbiNPxEvn6UWePw7hfWVienuNGcp8ZNoPTO6HU5L3QW/A4OSfMQlVi2SmJ0yzQiYk/2Xt6XECVnv49buRoCx8PpwKZCDmXPc5Xf1VIkFGjwpGQvGJz3swbPK42J0MMwqKjsTX7KtBS+8wbnhuH7734kGDuZHmy0nsSp41623ExfBQTVfUDKDVjbVDwx70M0KXt8iMKw7G8ir+0sr26Flixeccrkun1avZAcZ+hX0XiYT80xobG3W7hpqlpScih+sVN9dLM9E5YI/rW5TbjfC3vYNU8XusjE9jFVlQCyPl8+AnymfFfXCqESs/NnmoqdGVG9G//+2Vo4r3qUXy1HMQL6tsrNS5nrKOWukx2SRjZTxtLGzGFx7ZIfmto0M9yqYSRr9VaOMK33r3O8YiKdo3drCPSORY5fq0WtWDvqDqRJ84faU9bXbS3NyCxkb9B9onArSnRwXT/sU2OembUaIcx+HhjaXYNrI5tv7cEGZdkGUiQ8oM+QK2nqfAgouMhOKC2uytkee0OHG2Gx6//llZ8WBX6VwN5nOGcmUcwx13jOr13eP2ryLqwUhxnKp3ti2xeHZnZObzr3trcO/1iwAYk5NEd+cR60+9KyreQBDV7fr3sFR3DGgecCrkR9ddymiFlhajpp9/824B83fx+RtKfU++wYMUOY4TJpCGNPYBnmnsZa64u50+HEgBrYkFo2esKafjDPJ01aIbmsHIPlEt2a1q749LV99v4Tw++denpNi/R5nFO8eUPTzEr47FSk8yYnilp7+/H8uXL8e1116LnJwcuFwurFy5UnJPMBjE008/jeuuuw4zZ85EVlYWFi1ahBUrVqCnx9gBhPFk3Lhxhp/hOJMbkxm/Pba5zERKYRq7I7H47Z7l//2HxaqzdjxaA2GtfH1a2Iz3NdzBlBSv3YrH6IpZVmaG7nuHfPrOg9ot2/C800C4TcdXevTuwRqpr2G/sUAIdoayTTRue00a+njmzJmaz1itz4COM0yc6rzlee8btvdwRB7xhnm9n7Ly4xLc8Bx73x6ryL/11F60GZh8sEKij2GO11k7A+vmVfuZbrV6ZN32yH860ote6THXKJ1qZ3JDn/WaKTk5htK0uirVIDsjiCeWAZbErFRZEWVxRofhqNZObdmDrFEF/OVY7OmZNn26rv4qkTBs9HR1dWH16tXwer1YtmwZ857h4WGsXLkSubm5eOaZZ7Bp0ybccccdWL16Nb761a+GTwFOAjIy9A9cJRgUNnnY5ajromtK527Iceo8FgBo7bOn/tS+mQOHu97SH5ZSjljhL19v/MA7K6GkASBtzBhTz50bDA8AWZ3AzrK2hJ1dV5J4juOYM04v7lGPoNTSK5Ux593nHH6BAfScD6badnR8i9J+B0mgDO1kTCHPX13XEPN3e1+q77aKNmWXUb3Zq1UIi251wGMosE6MFcVjm8uYG//tqFJ97m32IBwAq+Neu2bSY3UwMkt8JkyYYDI1cwK2mxXZzczb9RjCDpTrzasix4TI8yA/nPSKh6WuhOFr1vOg9V2BGOy95Jk0cZKh8ywTAcPubbm5ueju7obL5UJnZyfWrFkTdU9mZiZqa2slhXHVVVdh1qxZ+MEPfoANGzbgX//1X63lPIExamGH9/Qot+K/qJxxI6Z32M+cQXcp/FsLpc/QaxDEYvbGFwxhS7F6hK2qdv17s6xiVak99GkJrsy7wJ7MxBA196GCxujVXa+GS594w20gGMI8i+GtY43Vvk1LjqxE/wH0+XuHOA4tvcOYnp3JvB5LO/HaP+/Ftt98w3Qm7MhrVfsAznZpn/PUZeHsDwCa56ZouYmp4ZTLy0t7q7Hy5kujfjcanZKFne5tdn69Wa8OVjpOEJ2unfueOEODCT0GuxGjvrCxV7Pw5UEbnObkiEspn61ORhApo4eqsqhoUx7PHKntwvonwntsYjHvESuD3U4MGz16BrJut5tp/V155ZUAgIaG+PjZxwodniMSXLLobWb5ydrj+Mf5U6wnNIKSOOs/s0bDvU0t7K7OtvTxafYZLVabYlET279cL0oHF7KQ57VOYWDFceZncPl263LFflVDvKqgN//isZlX554JFsmolGOBntPqn95WgW0lbVhw4Xj8/Ko5McgVUKkwQVHRNoCaDvOTF0qrL1rIS+kbT+wxnQc9k0WdA17cs46958aOdvuT149p3wTAzJDJqZYmt3luefEAvpM/A7d9dXbk3YzCsdKnbtOYSAPM7/uMTscZ5Omy5CdWfcHKT0ok9SXHaNl5AyH87wdnJL/Jz4577UCdwVT1we+lled5R2nY3VytTK96co+ud6ilobaH0MhkWCjECfuQzJJIHhJ6iWn0tl27dgEAFi9eHMvXmsZMJ8uZHGbZZZVrDbZDHIe/7q1W9K0V8/fDZy3lpaxVPbrYGZVzEPSWoWIYVIuNcX9VJ679817Dz9ky8wd2h83ButtdqoaSG/AGTPltq00gi6/pPVdHnAcrZarnU95XjF5m5b3sF+vaKxAKOe6e5FeYmRHL17aScDCU8rZ+/M/6M4x77UWraG59TXsfYbLDlzmLchXXOzmsCZs+j599cCSDHaXK+TCC3v7QiCydrO+J2ouh1q6GfUFsVylXFiveP4MntpYbesY0MVrpYZVRSO1kbhm9Q37xUaxms8XGRHJyF/5YTXD9/M3wgdVKCwCJHsqc58lt1uU7FAohZHSWP87ELHpbU1MTVqxYgSuuuAI33XST5v3FxcXIzc2V+Jx6vV6UlYU390+aNAmzZs2SPFNZWYmhofBgPj8/X3Kts7MTTU3hTfGzZs3CpEmThGvBYBBFRUUAgPHjx2POnPCs5n4NNwMljAp9V1cnAlPtjbAmRtw491V2Yl9lJx7dXIaPb78Uly0Iz74MeqM30687wR4MDvTr73ydRulAPjvUTp8ngI7O2Ic8Plt3FgF39J6gvt4+DAxqG6ssOtrbUVDgg9sFqG0bX3L/Vvzhpmg3FS1aW9kzo/Vn6zGY5Y76PaihKOvqrBncPHrk4L/eK8Cl0836thtjcFB7xeGFT4+A46wPKkpKlDfpBmw4oVwpKE1BAXulAgDAAW3t7AFof5/6GVhDw/aEzFZDrrsHBszpuqGhIVRWSs8GYY2R+P6K57mdyueJGIHlYvf9F/Yz7rSP5mbGqjsX/Y0sqquVXbhLy8qRFZiBGTNmSH4vLFYPJR4KhVBQUIC/lwfx3skWHP/d1bYO1Xt6e3G4JtJvmh3sxmqwPjQcXQ9VVep7K3nO9fThc4/twx3/GB4v7Chtw1dnsd1ezWK1FGIdJEspQmKimDx9/f2oq6tDXl4e8/rGU2dxz7WXGErz5ClpaPHSsnKk9GQhPz8fdXV1wrlPixYtwhjRvube3l7U1dUBAKZPn46pU6dK0ikqKkIwGERGRgYWLFggudbY2CicBTR//nxkZUXGynp0i5yYGD3nzp3DDTfcAI7j8O677yIlRXuBKRCInnHmOA5+v1+4znqGvy4nFAoJ11iWqVq6RjF6OCkXCsHJpqLk2tE3MojgOA4DDKNHGeebtdXZErtmW0Ih8/7zetlXITWsgsEAQq60qPuCoZDp7+LlP7wpWD2N/VXGDb1AkF1OgWAA/oDxPIvbYSxmzmLVUemZFTvWNAy4rU+CKOlCwMwByow0FL5F7b0AEFLYaKtVNsyzWByuOc7kHhhxX6WGkZl2q1R2mJsw0cupZnb6emReSX8AQHHbEFp9nbhDZvS8fkJDT3FhWewcCOuSYEhbWk7W6x84h0Ih/M+GyAqo+XN6zD2nI2XJ/1gTTXp1q2/Eo2JvRWSlkEuwGf5EWXGwQ7faARcKIajSrszk8r4d8oixkVSCwaCizhPrQ1aefD4fQqEQ3G7GBKkoXZZNYBTH3du6u7txzTXXoKmpCdu3bxdWUbRITU2NWj50uVxIS0tDWloaUlOj7bXU1FThupyUlBThGsvoUkvXCBxn/CTolJSUuIRsdLnd8PiDmH3vJrxzVP8+Kz1Ga7wx2hSUGk9KSnQjNJOOGq8eqJX83+1OZfraWpETtzss/24dVWdGabtc7HJyu1ORwlBkWrhF7dDK3utEczXQ03YONgzDo+P0eiX4L2bpQR7DZcoQO6VvUXsvAKQoCKFW2Vh17TSDy6TPO99XSX5j3Jfiip0udTtcfMdboleXOOiT+VQVHfHSiX48siO6f9pQElkZZDZzV1gWrQaWUMJlU905tqdHljCr/bx4XH11lYevQ/EKsZ3jADtE050g45JEObvJlZLCNCKE6yZKvaxLatRkZGYJR7u43W7F8bd47M7K05gxYxSfFafLsgmM4uhKT3d3N66++mrU1tZi586duOyyy3Q/u3jx4qhGlZ6eHuW2Jmb+/PmK16ZMmYIpU9ib/N1ut2q6RjEq9JOnTMGWEntCORph+rRpwgrP9lLtjZs8w9wYAM6FxAacj36llymTJwOIXfQ3AJiVOwu9w378f/bOO06O4sz7v560s7O7szlH7Wp3pd3VrnJCGeWAAZGDwSYIgQGRwUfG9sk+3nuxz4dtXo7D4fCBwfbZBGNjm2hwAE4RBSStUALltKvN8/4x0zPdPdXd1blntr7++MNquru6urvqqXqqngCIv0k4nIPsXg9wiJwPQ4nikhJ0dIyG93++AKCyoq7j3UXzPSSvvNbW1qA4OwP4k/iY2oAZNV1VztFEg7tUHiArK0v1nIEhcY4ZvbS0tADYpXqeEC1jSF5eHrA7eXW/o6MD+DnZNDYCoLSkFNiUbDaWnRMGIP/cfr8fOGPtzqt0pT87Owd6ZF0oFFJ8DzyZoRAAe6JMeb0eDBoICqKHSAQxcxTlZ2xoaAD+bK4pscfjQX1zC9b9PJpQ1WydL0cS7lmvEmDVwoy02GhbE48dR87QtYfMmEmRMKhMXl4e8JlZ6Ss4w2O20GXBSdwy5oRzcmRN2wAgMzNoWHGtra1FQ230vSvdKzc3V3GO3dbWJnusqqpKNhdQKBTCKY3uFpYpPbzCs3PnTvzhD3/AuHHjrLqVq9hzrFtzo3/xw72GwpDq5dGXN6OhOKqla9H6TxrIYsyjJuhdtkBPjRnVHopE8K5MQAq9A7eW76tnp0fpEtIhte8v2olI0baQarz44V7FyEBmIR/gREUmONAQzJyQOpR/MYFD/YjqHRp8N0e7ybs5onHV5PdPm0pCDeuit4lLNmJ2xcvjfhtzwKQqbrMuUEI2EBQlYypzTaqJfehSel577TV0dXXFNazNmzfjxRdfBAAsXboUHMdh0aJF+Pjjj/HEE09gYGAAH3zwQfz64uLi6MpOGvKzDz5DVkCbOY8TCg8AvLn1UDyaj5YJheODNwVaTQzdxKsbPtccbUgN/pvRfDo9MltpQNWnRCWuMTJY015q9kAlV5xbW2V33wDu/MU6W/r2wVPinRO/l0O/zsAKcu957WtbdJVnN3aKUkeURpvuee6/v5f0W3ffGqFjEgAAIABJREFUoGhsNds88lcfG9+JBlJjge/mn0cThYvTD5j7Po902ZtXxyrc8j3/sfsYznvyPfxy9XTicY7j0Hz/7wzdw8wcWnahS+lZvXo1du9ORFf6xS9+gV/84hcAgF27ouYUf/97NB/ArbfemnT9VVddhWeffVbPrVOCLoeUGLuwpVMbvEd3n/GAFE4ht5r2yvoDGG1DlDE9ExUlHVNPexFeojXZrx7UwqunO/z3k09InDocOd2LH75lziq8uTj7FvUqlkYwK4Enz8GT2kwNjwom0mYr9NKFErf1kc9PSpQIAx/i7VgAA1LyczPgANz63/+rel4q4JZABqd6Bkwxk1bCbW2eBl1KDx96TolU2uJj2M8V//FXS8s/1aNN6ZFrrdoDImi8gEDQR94pPNkzgL91avfnAbQJJz1BcJQEPdG8TaU8YXFWZZFPV3QpmTou2mEgWaj43nTnfSGdxMkw4RtvGKiNvbCWrY1rfvwPTecL25bZEzS3i6W3t4n9hM2orlVWKRwXzQOUDnT1DuB/9xhTNj6VSdKsByun4jt27oDf51P053EbtuXpYaQPe48Zd158TyUHkjSimVYG3D4iKaC006JXgGlZ5dSz0/OWTNLDSETfhFpYBzt2esxGSyLJVGXTfrrIT6mM3qYXiUSozH/SfXEwAnMnXUc1RmKzcxhwu9m32W3tt+sIeZkUqLv3FcXjTphfWsED/7PJcBlyaUb0IPdW+wz68wDA8WPHRPl4UgF3xPhjMCR816QkfXaTDoJbz0RBbgdqYCiiz/ZdUIeTZ1LXVFGKW31N7Gy1cnNDo2aQVqAnZxUQjXKVyn6FZkE70baqjwt3oK1OC+FESHUtuLk1cjAevS3N1w90I9cHdxwyrlg5kWrFKGynh8FQIN0Eqd2rzz95vxPr954g3ESlDoK/73lpvWn1YTiPdLBN5V1ZOUY98DssG1Mu+o3U9dLvyZM5LhNZTcgNP/uQqiwjsmn8Y3/QfW064PaxzOXVs41zvv+u01WgRksaGrfAdnoYANy/SuUUP/1gt/pJQsxITGaB9P/3P9M7dpt5/5NnyHbaO1W274UrtJ+fsDYnFMPeCRGfG8zJOtjBKxsOqJ6Tbs8sJRIBDpjUfyMR7fvoX2gMfJDOuLmpcZx7AgA4DXGR0ADCt2p2gJdAIMDM2xgMRmrjhsFHWIVU9OlxA1uHeUQ6t7Hqp8m7Gaxl07Np/0nNSqKdEcHcbunjev8xo+ZtrDcREX52t5pX2wlTehgMhggzh47OI92G68B8I7Sz5fOTWPTE2/QXqLxit07o3D6PU+OUCYmehwuDQ5G0yeXiBHI7rG7BSFeORCKOhGRPBdywiOkmmE8Pg2ESg0PmrDU5LaLcoGMIVyUHWBZwjURw5LS2KFdm8vFnxxy7d6qx0wRnYjdDShqqlwicyTVEi0vXBeK8KRNh0y0Y2Yn659e24Km3d5pYm/TByt2d48ePg+M45ObmWnYPs2E7PQwGzFkxbvj6q/jJ+52Gy7FqYaZ3YJAqaasbzCCENXCDEpZqODkBO+/Jvzh4d4abONLV5/giDsP9bPn8lKF28j//qyNC6DBBbwRKGj799FOqvJ1ugik9DIaJvL7pC8NlbNhnTRblC3/4Pnr61XdNXKDziLQetj1vPW6wh9dTBzfUm6HMsNmpdasNaIpgRMyzQEzy9A+X/kcJM29jMEzEjEzKtJnntUIbFcYNSoawDlZlAWckUPvkbFLB0Mtw2allPcQYnx3V5//JUGbAQpPQyspKeL1ey8q3Aqb0MACwRSpGgk4Ts0HrxQV6V8rixiSfNOiqtxsqzmAwGC6lz8KdnvLycvWTXAYzb2MwGCK6XLCzwuayBtG4iOEGPy4Gg8FgmMuwMS+lhCk9LiAcdH7DbbjPeZhvgLvYd4yZOtgJa/0MhjGYtYRzfM6S0Mri5oiHTsCUHhdQX5ztdBUYDFfx8G83O12FlOXjPcc1++Co+vTYMKFjQzODwWCYC8tzJ4YpPQwAwIZ9dE7uDAbD3Rzt0p6jR22n0607wS6tFoPBYLgCKwMTffTRR9i4caNl5VsBU3oYDAZjuOMC7eHFD/c6XQUGQzcswiHDjVi5YDU0NITBQed9gLXgvDMJg+ECPth51OkqMBiOoTYuutVf4fMTZ5yuAoMBAHj+7585XQUGIwkr/ZWDwSD8fr9l5VsBU3pcgFsnFMMJM/LrMBhuQatMcav5mhpHu/qdrgKDAQDYf4I50zPch5Wyva2tzbrCLYKZt7kApvMwGAwnSdXohb39qWVawWAwGHbihmTjboIpPS6ANUkGg+EkqTou9rIcFAwGgyFLiop2y2BKD4PBYAxzfvbBbsXjbt2N7h9gSs9w4fwn33O6CgxGypGqC1pWwZQeBoPBSDO0KilPvrlD8bhbx03mDzl8YOlGGAx3sXv3buzdm1pRN5nSw2AwGAwGg8FgMKg5dOgQjhw54nQ1NMGUHhfw8WfHna4Cg8FII7hhsgXCcqMwGAwGgxYWsprBYDDSjH3Hu00tz6124R62bMdgMBiOMHr06JRbYGNKD4PBYKQZtz2/ztTy3BrS+i87Usu0gsFgMNKFrKwsp6ugGbZOxmAwGAxF3LrTc7ybJSdlMBgMBh2alZ5Tp07h7rvvxsKFC1FcXAyO4/Dwww8Tz/3oo48wf/58ZGdnIy8vD+effz527txptM4MBoPBsJFeFhqawWAwGCmOZqXnyJEjeOqpp9Db24tzzz1X9rwtW7Zgzpw56OvrwwsvvIBnnnkG27Ztw8yZM3Ho0CFDlWYwGAwGg8FgMBjOcPr0aXR1dTldDU1o9umpra3FsWPHwHEcDh8+jKeffpp43oMPPoiMjAy8/PLLCIfDAIAJEyagsbERjz/+OL797W8bqzmDwWAwGAwGg8GwnS1btsDv96Ojo8PpqlCjeaeH4zjVaA0DAwN4+eWXsXLlyrjCA0QVprlz5+JXv/qV9poyGAwGg8FgMBgMhg4sCWSwY8cOnDlzBu3t7UnH2tvb8emnn6Knp8eKWzMYDAaDwWAwGAwLKS0tRXFxsdPV0IQlIav5DK0FBQVJxwoKChCJRHDs2DGUl5fLlrFp0ybU1taKdop6e3uxZcsWAEB+fj5qampE12zfvh3d3dH8FNLttsOHD2Pfvn0AgJqaGuTn58ePDQ4OYuPGjQCAnJwc1NfXUz8rg8FgMBgMBoMxnKiuro7/3dnZiRMnTgCI5u8JBALxYydOnEBnZycAoLy8HCUlJaJyNm7ciMHBQQSDQTQ3N4uO7d27N65TNDY2IhQKxY/x830tWJqnR8kMjsZELiKJkxqJRNDf3x8/TrqGPy5laGgofmxoKDkSkVK5DAaDwWAwGAwGI5nBwUHZ+bdw7j44OJh0vK+vD0NDQ/B6vYrlknQCrVii9BQWFgJI7PgIOXr0KDiOQ15ennLFfL4kxYjjOPj9/vhx0jX8cSkejyd+zENI461ULoPBYDAYDAaDwUjG6/XKzr+Fc3eSYhMIBDA4OEi8XlguSSfQiiUz/IaGBmRmZmLDhg1JxzZs2ICRI0ciGAwqltHa2pqknGRkZChGiWhsbJQ9VlRUhKKiIuIxr9ebUtEnGAwGww1wnHsTlzIYDAbDHurq6mSP5ebmKs6x29raZI9VVVWhqqqKeCwUCuHUqVPUdQQsCmTg8/mwYsUK/PKXvxRV6LPPPsOf//xnnH/++VbclsFgMBg24tGx0sZgMBiM1GfDhg1xP/tUQddOz2uvvYaurq64QrN582a8+OKLAIClS5ciFArhkUcewaRJk7B8+XLce++96OnpwYMPPoiioiLccccd5j0Bg8FgMBzBwwHJFtoMBoPBSHd6e3uJPvJuhovo8ASqq6vD7t27icd27doV3+b68MMPcc899+D999+Hz+fDvHnz8Pjjj6OhoUF0zdDQUNIWVU5ODtH3xk7q7n3F0fszGAyGmwn4POgbSK1Bj8FgMBjG+fUllfD7/WhtbXXk/np0B107PXzoOTUmTJiAN954Q88tGAwGg+FyvMy8jcFgMIYlY8eOdboKmnF2K4XBYDAYKQvTeRgMBoORKjClh8FgMBi66O5jHj0MBoPBSA2Y0sNgMBgMBoPBYDDSGqb0MBgMxjDjiqk1TleBwWAwGCnMvn378PnnnztdDU0wpYfBYDCGGY+cI58MjsFgMBgMNQ4cOIAvvvjC6Wpogik9DAaDwWAwGAwGI63RFbKawWAwGAwGg8FgDE8aGxvBpVgIT6b0MBgMBoPBYDAYDGpyc3OdroJmmHmbAYJ+9voYDEbqkVprcwwGg8FgGIfN2k3m5nkjna4Cg8FgMBgMBsMlXDihyukqMMCUHkNwhPXS0nDQgZowGAyGeby0errTVWAwGIy0wZNivi809PT0oLe31+lqaIIpPSYT9HudrgKDwWAoojb+TqjNt6ciFpAf8jtdBQaDwRCRhjoPNm7ciC1btjhdDU0wpccA6diIGQwGI5VJxxVVBoOR2jCx5A6Y0mMA1oYZDAYjyr1LRjldBQDKk4v64iz7KsJgMBgxUi20Mw0FBQXIz08tqwCm9BiA1IjTr1kzGIx0weuxTkK5RfYp7fSMq06tAToVuHRyjdNVcB3XzRzhdBUYLqOtIvXCO6tRX1+PmprU6v9M6TGRNFTkGQxGGmLFqqNb5J+T5m3nj6vEBcMuSlPE6Qq4jppCtqPIEDN/dInTVdBER3We01WwBKb0mIhLxnwGY9gSCrBAIkqYJaNKcjIIZbtDAqptZmWxNsKwGAs3VBkOUJAVMF5IirWJ/7npLKerYAlM6TGAtA0zB1oGDXctasZvvzbD6WqkJb+6MT0FtVmYJaLOHl2a9Ntfdhw2p3CDqO1iWSmnh+OeR2Q4PrQKw30u0FiSbbiMa2eMwOo5DSbUxjhDrJGnDUzpMYJErg1zOceg5Ka5IzGmKrXte8dUurP+zWU5TlfB1Zi1G0OSdRPrCkwp2yiqcthiOe0dZgMBmw8mM7xagDV4PBxmjCxyuhoAgMEh443cLTvhZvLJJ59g+/btTldDE0zpcSHnj690ugoMhiLDz28hTbBw3B3lEoVTbZXdyqkHh+hkjZG6TDZBeR9mem/aM2SG0pOGbaKrqwvd3d1OV0MTTOlxIRdPrHa6CoxhRjHBR0MJswW4KTbTDFUsnfCnwKAeQcTS0LFs0yP1qczPxNt3zTVURjqGJ27XYJ2QE/RZWBP7MUHnScN9ntSEKT0uJB0FJiO9MNukZXyNe0MJr5pd73QVTMMs0UIqxi1yK8JUD1tJx/edaTDYRTr79NAoNH6vOVNLs8oxCvPpITNx4kR0dHQ4XQ1NuKNFpSjpLNgY1uOWZI5mU12Q6XQVTGXmyGLH7m12Mk2z7MpJUwC3SEOl+QkHzlBkrfoiFoo43eFgPPqaW/qCmfD96s6FzarnmjU1mlSXj8fObTOnMAOYofQ4vSjErCmiMKXHAFYm+ktnWivCTlfBFaRyeOWIwiBQkhPUXB7rSmSGy2u5ZFK1acExlOYnRs3brmFJJ5NIx0VwvQua54+L+uOm+nroJZOSTeydeCaO43Dl1Fr7byzBnEAGYuyePz60osXW+7kVpvQYQCoY01H4M4YHWsWvUlNXUoicRGv4U34C4yRmrw4Kx9k375yjuxy+GGH1jOx8L2orw92L1VeQaajMU95pNPJGL59Si+9eMla5/BSf8A57OP1tuSw3uuCT6lYgGT5jU8N0i1Rmik+PNNqv8SIZOmBKjwGMmJuSVvkfXtGC+5eNNlAja3jiYuVB3o1MrbcnfO45HRVU55FWsVN5u9mleo0iuZl+TedXqEyeUxGhElWVr//5iOZtLhnFi8PKQTmsrKdbFX6GNjiZsX3KCLpxxS19QS9GW3GqPz/gnmiUZmGFed3Bgwdx+LA78rPRwpQejXSuXRb/2+fR//pIY+PFk2pw7cz0cZp2EyvHWxNimVaOkM5bNqbc3MowFNFiopBOwQvk8BlYtSEGMnDx2qVPZEqir54Px8xDnLbNl3LL2Y3E36+YWiN7TdjE6FrpqObJ5Vp6ftU0quvd1ka0wnR387+hVD7a3USsuN1nn32Gffv2WVCydViq9Hz88cc499xzUVFRgVAohFGjRuHRRx9NubjechjQeYjwnSDF5SUm1TkficsuAWNkcOA4Lu1WkwD3ToL8XvpG0FphffJVmp0ns5ut2f1ApErIlE3yD1AqxwqEddP7DgqyoztIbhPPV0+vc7oKaUU02IW+r8zLvlT3USRF5NPySKk+h7EEh98J+yZRLFN6Nm/ejOnTp6OzsxNPPPEEXn75ZVxyySV49NFHcemll1p1W1shrQaxhgUE/c466AcI9shWDUK0E3y526eq7bcbFZv/9+WJiscLsrTlIrIaWlMZMzGrtfHfX7gaKtvGKTvfqDJzApyo7UI5MSHVonBr4ZJJ1SIz2Sm1CWXdrp03t+4K/PZrM3Rfa1Qsp6pc5yF9Uy2f2c27vrSYbaqa7NOj/o58JgorK77JiBEjUFMjv6PsRixTep577jn09PTgpZdewkUXXYR58+bh4YcfxjXXXIPf/OY3OHbsmFW3tg3pYB4B/QBgVW4DN+wcqG0LWz1IbvvGEl0CRg9GBaNbxkat9VB6bqceKSsjWdkWdlFNK5Vwz7cxylkjC+N/q/XNf7mgXVV5BMh9WK7sr55Vp1oeoD1BrhyKPTKiXxYY6evv3TNP13XzR5dqOr+22H7579Y8PWM0JNMUwhkIZMA3kdTf6TFOc6nzcxEjWG6iSFG8mQvIVjxOYWEh8vOdt+zRgmVKj98fNd3IzRULnry8PHg8HgQCqevEzWNkNccNq2O0jsxaBzWpwM/0e/HAcmfDJVpm3mawAukysXYDZiu2buijZrSPq6fTh1m+cGI1FrTQT7TVzNvKwkGMLFGf/NjpA2H0Vnqu15Ps8p+WjsY3z6PLUZIXogvScelkc1Zln7x8vKbz3bAYpwXjSou4gIsnqpt4WsHN80bquo64qKHheo4DXqD0f3IrppsWW1w+zf07JAsB/3JBu821cB7LlJ6rrroKeXl5WL16NXbu3IlTp07h5Zdfxo9+9CPcdNNNyMpK/SRvZpu32T0Bflfn6qMa0seozM/ENTMSEy9n4v1bVDDlxDgoEwLULWYAbqkHw3yEX9atK9C2VYtz3LSemqr8TJSGlXNe8XKNZndOeL5RJdMNCwJWYtQ8TXp5UY55i7yLWukXJWaMLNJ5l+QPrPWTy0XASxWyTQz2AST3OdsDGXDJ31BrRNN0wNyvKqCurg7vv/8+zjvvPDQ0JPJj3HLLLXjiiSdUr9+0aRNqa2sRDifsvHt7e7FlyxYAQH5+fpIt4fbt2+NBEjo6OkTHDh8+HI8yUVNTI9qSGxwcxMaNGwEAOTk5qK+Xj9w0MDAQ/zup0WoYCUhn2j2Q7Nmzx5Jyz5w5k/Tbzp0743/rMROZUhXEX/f2UJ8v/TZnupPrZAZdFEE5HljegpmNRVj4f98GAKxbtw5AtI+UhjOwwQXBT/r7+zWd79ZJT29vrynldHd1mVKOUbR+FxLCfs4PvAcOHMDBgweJ5/f09GDr1q2KZR45ciTpNyMTRY4TywiziUSGAERlvV74d2fXAkHn7k6cqAlhZEk2Pj14mngO3w+9sRHl5MlTwqNJ5/PfbWhoyFDdhLv/fX19quf39NDLbrPg5axWTp08iQ0b1hOPqYXn5fvUwS++EP1+y9mN2LrnMN749ISuOgnREkq/V+d7z84wNjXs7u7GpticSi8njht/V3q5d8koDA5F8LddR00rM2lMiXWhe2cUYu27yfIUMCavkuEwJBm4leZiJBkvha+f1+tFZ2cnTpyIfrPRo0eLrLlOnDiBzs5OAEB5eTlKSkpE5WzcuBGDg4MIBoNobhbna9u7d2+8Lo2NjQiFQvFjeoKiWaaLd3Z2YsWKFSgsLMSLL76It956C9/5znfw7LPP4tprr1W9fmBgIOmDRCIR9Pf3o7+/X6R8CK/hj0sZGhqKHyMJfKVypXXgMZJR1w0+EeZ2KCHJz6b2XtXINGjaapXdOY0Cd82MEcgPJQQA39YikQgeWtFKdZ+WcmUn7ysnluHC0fp3T91ql68VxX6loWNJBwenMKMag4OChZr4b4OyChUvZ5XgZagZUdF4jMoIKiL6dzk88V0SxeKJyN0zLyg/BA8MDCISieAyCpO0HTGFsb8/oYAIlTM+kALpu+lB1C5p2qgD/UnvgsFQZEj2WjVlcWhoUPRfngyfF1NrQqRLNKPlVfLKvlZuX9CMs+oMBBaJRDAwYGzBZkhn3c1gUWuZbfeqsMnoycNpazvStl5flFzRjz/+OL5hwI8ppL4jnLuT5p19fX2y1wrLJekEWrFM6bn33ntx8uRJvP7661i5ciVmzZqFu+66C0888QSeeeYZvPXWW4rX+3w+wnYgB7/fD7/fD58veSXC5/PFj0vxeDzxYx5CrGmlcqV14GknOEqSIoc1FSZvbZO+ld0TLa+XTpPQWi3Siq/ae1Ut02B8cOui6SSXOyLPhxcvKEU4I3FMqFTwbY3jOGRRrKj99JrJ6rXgOHgkeVdqCugHWeEESU3BUkNPKzbr8yhNaKXtOFPBSdQt0ZfMqIeX0Pe8Xi9RTgIJOasER+iPSjVVyhnDY1RGKBF/jZz+tka7w6Ol+EvG5Mke83q9qgpa3FxN5T7xHSGz8yyArr/TRvAzE7U2LIc3NlcgoTYO8cf9vmTZ4qMcb9XQMk/wKuTiukXB3ycz4MWKNr2mcVEZkqHz/fN4HLSPUwtk852V2n1h5MzbfD4fHllUKzqWFfBiXIW+5NFZMv6DHMdpChYjbOuT6wpUA4PwYwqp7wjn7qR5ZyAQkL1WWC5JJ9CKZa3qf//3f9HS0pLkuzNp0iQAiGuHcrS2topM2wAgIyMDHR0d6OjoIIbJa2xsjB+XUlRUFD8mjTbh9Xrjx5RM2wDxwFxbKH62CIAlbeW4f9lonD0qsX0n3I4TnitkRFGW4iTMCqqrrXGuzCb4a4nfq/aGmp+vLbyvdIJCqpMZBDOTbe5zQwGEw2Gx0BZ8cL6t5ebmUr2J8TX5qhO1zMxMlJaIbb21yAOtEwSzd4bM0Pc5LiojaBGG+pWSle0On0O9EzchtTWJfs63ifLycqKcBIBgMCh7jKcg1h85cPHFH1J7438rylb+Lhw41NfXWxbGmx/AvR4v7l48injOxw8soCpL+pjnjavUfA1PRYV8guK6urqkQEBy8GNMhsCkRKho8BPlwkI+kl/i2L9dOo7qHkKE3VUuKJHQEiIvx/7+pNaGpdwaS/IaDodlry0qUlYEimNmO+Vlyd/17HHkJLJa0aL0kOYeU+sL8I1z23Dj3GSlRzgpNhKVKysrC+3tYsVAa4Lw3DxrcqWtf3ih4TJoFiulSOcg/ILW6NGjUVgolnsPLG/Br26ZR70wLeSv/zSf+DsH4ImLx4p/U5gkJGSFuL5CwuEwcnKiQUrq6uricxupTMjNzY0fk5q2AUBbWxs6OjqSTNsAoKqqKn6ttD2T2rcalik9FRUV2LRpE06fFtsiv//++wCiD5IqjKmk73xeD4drZ9bDp5KXQSq47ljYlLAZd8cicxyt9bGy/m57N6TxJ5SZiaamJpHAkjOFVGsnAP0zG9EbhPVzqbWKKvwT/OmO2eTjGtqOUGl2W5tzFaLAAMZf1POrpuHlm2egttAcUyApEQBtFeSdzHwFJRgQBgEQ/768XV5xUcOsplVVFVW8cnLIzzYk6a/Cyc6KjgrN9xOalZidz8RKzhpZiCun1hKP8d/RkM9W7FWQZEZ1QQiXTTEePU/6LZUgTVSDfi+umFpLXqQwUK+ksiSFucWEOhykSApts8yX60J6+pacPxbHAXkhsYyjjz5L/rmpqUl1o8BtWKb0rFmzBocPH8aCBQvwwgsv4E9/+hO+9a1v4fbbb0dLSwuWLFli1a1NZ+6oZM1UC6RVzhQaJzTXVX/EGHVKdObykLOuMFpX2ldTKLPSnRP0Y+35YwzVAQBGlmQn/ablu9EoX6KyFY7pGS/MHGTqi5PfBQnaAcXJvjqnudhwGWY63n/1rBHJP5q8WNNWSbcDWqeiGP34q5Px7ZXG+xaPnAyRPvdtC5pwxdQa1d0tK3CTgu6iqsThwOGxc+nCgBtBzizVDFmipQylb2BlQA4juY7cABf7H89NcxuQLwgLr+fRknIHxgOjqJ9rBoYiCyO1FjeUsEzpOeecc/DHP/4R4XAYt956K5YvX44f//jHWLVqFd5+++20yNNDS8DHOZKn5uEVzuTGmVpfiM61yywpm9quXkbACLloYpUltuZahcslKo7Kas88t7kYF0yoMjSglucmzPSMvpH0EI3uoKk0x+S+ZOzrnj06ugAkXLWNO/gbKFfaZ1bPaSCfGOPlm2fgD7eTd/R4KvOCSck9jT09J/kvmaLsDHzj3DEQulNYn+fQ3gkmjaxpldlRE6IlJ5TVmCm35L63GRNHLWUoKR6WWmSQ7p1iA4Ow+tfNrMfHDxo3ixNSlB1Iuo+VsLQUUSz1FJs7dy5ef/11HDhwAN3d3di6dSsef/zxJFvBdETYwCIRZ7TkslzlHA9WodaJvzxNbF5wj4yNfSqg9FntGEQBoK4oCxzHJZkP0ArT/7x6Er5xrrYVcaPN2YpkhXqcGn9/2yyZssR/P/qlVsw1YdfFESTPIsc/LR2tWhRv889/f05QvJHcL9IrL56kvBAQ8HngV3DSTi4/egcz+mQqLmDzPqZm1V0oa0jv9NVbZuLqs+pUy6FNkG0WSs+fF8tZ0lZJVtam1avPW/h34ZqdHhNN2LRel4LdJL57nLRoKnkaM6wZ5Kw/LMPAB5lSX2hrAmkrSfH0UfZw4vgx2WO/unE6fnhFcnZqp9vHMgN25sZRFhCXTK4RZRpfPadBtNNw7ljtNuaqNaJcefvuJWPJJ8pAUmbPnOlzjJGvAAAgAElEQVTB9u3bTQsJbnVbmjuqBOHMhB0wlU9Pqi3byUAKw0niy9Pq8KMrkxNAhmQi5dCypM2+0Khq1BervwuyKUb0V9KmqVVNV65csX8KZ+pATbMpLDch1bPKypdF09P2748m+zp16hTx+FNfnoht30iYlPOvRe2Zfn7dVMW6Sf/mqSkMuXJlWUlhKAkH8d6983CFjM/Pz68nvwsSsuONCXJTSyADpeav1axKS805jiP49NhL0E83vRUquaPKEn+XhuWVErn3dP74SnznAm2R3ThwtrwbI71xzdnkIBzbt2/Hrl27DJRsP0zpoaBHIeHhuJp8LG5TVzCMDL4TaumjqPD3iQZfMGfQUcsKLkU6kJI69OVTyAMLkBwVDzA+8acdgJUietEyODCAEydO2L67J7zdbfObNF3rFbzgDELYdaV7aTkme3+LQtqqVUVuRZa2Nk2lxnasfnDFBCwdI6/4mDFnpyniP66aiLNHq5saWeb8TFGI0EGX5MMGyEciM+U9KtjgOw2f+LBPJr+M18MR0ymo+V3ITRxp+rjWd/79y7RHkdOKmsJQmZdpiqIsN96YstNjQj2ARHuuzzc/VDwHY3Meo5SGM6jmTT4PJ4oqJ1RKzx1bmRiXFB5FmOLhXy8ai4smkqPimrUIoMdKwuvh0F4lHx5fDTk3gBMnTuDkyZO6y3UCpvTYgHZBJ25gXh3CIxLRN9Dfu0RsalZbGMJZGp399Qg74RWZhNXzv+6KZuQ9029eQlUzhJAb9jtIpju3ztcWHlX4zVaOVw/By6Ml7r8SpuSjUZFmpJVHTRHdLBrD7dSN5R6hWkNOJyDR1jgu8V7MXtkfXyMepIW7OLQyhrZGNMVpNeNbo3HhQR/afDbisiL2AfX2O625SWXLiQCrZkejP+WHzPfzfebqibhR4B9mVy48uddqhgWGlkkvKa1QkvIeeyVqstxqFebuxeJwxUYThNLII7kAPlG5xmFqvVwIfU50LlV9BOc9KPDx1toFr59FHy3th1dMwMs3z8COby01ZUE3HWBKDwUlxXTR24Ti1GnzNr1cPb1O9O82DeG6eXySVQEtr+Jn10whRmXac/QMAODEGX1Znq3KjUfazcnOzkZHR4euGPskqENWGxjP+RxR9y0ZBZ8GXwnSPWnrK8yXoGenRzr4kxIvCksl19VYw1B65dJ+4BRWrLgK3yU/uTD7NqvnyCdPpEHkl6V2rpZyKc+7dHINKmJmu7LvxqSX1jAyOrHPz6NbzZULvy3FahWhOCdD1E++QuEHpIV5o0pxqSBQjJZwz0aQUybnNKvPJZSi/t2+oIkcQTGGNHiE8k5P9L+ZIbJflVReajNv03Ayge3fXKLJwmVSnfhcsyLcxc8xWbZ9dYb4G1plFbK4rUxxDmdU7nV0dKC1tVVzvZyEKT0UqGVhJiEUNlLHfUCbA6ceO2COA3KC1mU4V0I6gdVS+xmN5oS7tmtrnfRsHg9HzB7sZjIDXnz8wAJNq0g8en2whPkS9Oxm8ivERspwO2qP9Levn23ZvW+R2HFH/fCkCxrJtvtKSBXVptLseDlOQtNXdQwDtsEvsHg1LFgABnZ6VCZptKXqkTdGsNrk2Izy5XcXgJqCENHUiDdnbq0Ii1b0ldZdEnkBufi55vXD5HLU3o2RV5cUaEDTDn7i5HiAFpUCrB5qtPjzGcHoHMXv98Pnc2aeqRcXi/HUhjfRev++eZhOMA+7YbZySFaesE7FJRKhizYjRdoHmnX4LOhZ4TbS+X54xQRMlmRyl5ZGNPUwQXAJBfWPvzoZuZl+rJpF921pURuIzBLA+VmBqAMqxbmJASyCUeVhyTH166WRt/R8f+l91IqQHpdzWJa9XtPZ9pg+llD42wnrLfeOagjmbSOKxL8J/fD4hRiheRvx3jIHG2M+OVbn8qA2PaE6h7yjZWSiKMw79oZKCG4lSHWgqZeaqJZPmij8W1tLn96QGJe0ROAzA7tMfKxq1pNGkBWieH8Eh1dvmalYD+lPFbnRBVhpX0xu5/Zh9F60izEcOGJSYv5SM3VkJVknTRqql6e/nBxshyGGKT0mIuwgDyxvwcMrWlCeS97RoR3szxGsov/7ZclR4pTgOM5QcsM3bp+Fm+ZqNzGRrkRZLSxbK8JJWZalq9TnjqP3U9GCUCbObirGuocWxnerzFpVjCASn8Ao2V3bGVGNf7SKPH0hZ38giXjIK8p3LGhSzdEiB8lETumNKLVt2klLA2X0N7cgNxEO+ulMMWn8RLSUs3pOA1bPaUhatLASUjWpvjeFSZiWHvjS6mlYKMhTo2Wi/Nx1U6jO++Z5bfjFDdOSfudvZYbSqVXqjK3W71CtB+EjXjWtztJ7WRmoINPvRSWFvBWmqlAzP37uuin4lws6ACS3BTnzNppxzelNd7WxcJ0g584KCj+rpEVUHXWSM+HmOGBWYxH+8+pJOko1RvrZRqjDlB4Kent7NF+Tm+nH1QLbW2njop2gCicps23IEyK838iSHFFHzQv5SZckYbcvA8cBs5rEu2lSe+Aywoo4xxkfpEgDwPHjx3H06FFLTCnevHOO4TJumN2AiQr20rQD1n9dO4UoqGmur8qP7iJMqM3HlBEFcUX57NGlSQosbT21+AW9fPMMtdIJ90v+7f7lLdj1z0uJOXxI37+REHVMqZk4afZFnDARzuNfC0mmTZGY6iScqKP/zQn6cM/iUZZE7+ME91E1VyE82bfOGyM5Rx2po7ww4IOQuc3FmFBbQLXDSWpHUqd/PlR1b2+f6PfLp9RiUl3iGyS+FbletEQQwX9fPxU/uJy8EKel3IKs6EKO0fDvapw9qoRodaFGdUEmrpiqnDdKilsmk4MqY1BLoQ+93dHoW2aabxreqbFYa8oVzGVI91K3GjC3fhzHYe4oSt9xE6cVmh6DcO7Ro0dx/Phx0+pjB0zpocCKj6o40ZE0LmEiQK1ovcaMviydwDSWksPLmgXHcbhSxVSJJKTMEB6kcnfv3o2dO3dicHDI+A1o6sD/Qfk84UwfxtXIr7bSTLQjAM4aWURMsKblvb60ejqeXzUtbmYzFIkoLggI/Xik99Gyaq0nQAeJgphJYBlhR5eYtPHWmYRf5TEn1LLxMpIQyKT4RFrywH/9+tlYe75yzgpFR2sD1ZMjEonEy20ozsJbd82RvdllU8QTXanCJle+Xow874ED+wEAXadPa7qXXCjaBOTniUSAqfWFWDKmXFbuCGWj0iTx6ul1eOrKCRhXk6/opK8XoxPUd+6eR5282Q3RPIUMqkRu2L17N3bt2glAXX4a7Y8kMzKzMHuOkewjlPz0peEM3e4HamXrxe72t3PnTuzevdvmuxqDKT0OIW2cVq3oau1Q/NlGVt18kiWjxy/sUL8vre29zHlqz2nV5hNNThujSN+nHLQCz2mncRL87uDgUERRabpvyWjZY1bl+uHRWjrpOZwKtiCXaVwvokiVsTcj3eUoDQeJuWHMrActpNt1VOfFc4JpsG5TPHlIss6haSFV5qVQ7QYRr1O/p/pCAfl4BmXiRx4lZdDr4bAwFp5Ya044GtSe0C8TttjQPS1u33+5dx5mNalbfpBfO7lyarLJaPS2ibXWmbA+uKJF9G+9Y5zaMzYUJ+TFu/fMw4cPLNB1HyMomtdqWHTZ8a2ljpshOgFTeigI54TVT9KKjhVBOxooP8DKVY8m27B0jh4KqK+G/PCKCbhGEsaRFroJC4f//IrYFIvjjPvBkJSeiooKVFVV6Yr6R8LrSThlKrUBs3YvaFBqvqPLtfeXiyfVIDvDh/piso/Mc9dNQefaZYplmK3zWOEjRVpZt9oXS/cEQCHEt3BwrYkpVDRKp90Je+OPTqqaoCo0u4Q08lfWvE3HN+DbBc07Ky6OToBDWdryLSl9stxMv2wS2HM69PtIKge+0F2sbn5901lJY4NRzGzm371kLADxu6nIy0QtIfiI9P3xOz1F2eRdloqKClRVVhGvNRtS+VseWxz/W9jOtVYlw6dvkVZ+EZWvk7g+545NtHu/16MaiGP9wwtx/7LReOzctqRj/POasZhG4qyRyoGsvB7O8AJoVVUVKir0RW91Cqb0ULBsfJ3l92ivIk9Y540qIQ6c81TsP/VOpNS6gFy2YSH8zsRt85uoE6m1VebigeUt6icSkBNc0rDgJSYl0hRCcgAvLi5GWVkZhemIOfDPf04HvfBREpzLO8pxwYQqRd+s0jD5Xb5z91xcPkWb/TsAtFSEsfGRRciR8eeZ3qBui6826ZYT8OW5ZH+v4Q5x90D6b47Dg8tb8MKqaVSLG3bCcVx8Fb+3P7EFo3dXJO4fpHCOnjwws5qKkU/pLwkAv79tVqJOscrk50d99IJBusAi/GRNaRfphtkNyM3044dXJPvtCPsaaayRTqecDN+vduuqvBDmUuTPcQoa2ScHr4SHM4U+LInjxcXFKC+L7rJ5OOWIZ9rcP6Jn/26NsjkvbQAVrRhdSJJ7Vq2+cOGgH9fOrFc0v6cp652759LdMMan31yCn36VItiJho9KGj/LysriCy6pAlN6KOiwINqMsEuGgz5iRvSvnFUn69wmXYH79kqyzbGdPj3javKwoqMivnp46/xG/G7NLOWLTEBuMvvLG6cjOyM6EeOILd34QHzfklGyx4yIXTkHYTNQ9pqJ7sw9fmGHoonjyglVxN9J7VgrencDlJL6KSEXEclI7gc3wXHAo19qw5QRBZpaPE2kKCA6cYlGX6OJ6iSpgaZ3qr1dhAI+jCrLwZoFjYrn0VSjJZb4UWkCL9d2ldrOT746GR8LokkpcdeiZjQppBHguKjDPkB+Jv433jyNpq8tblOPbmUWeroYbRhqK/tvoaQOhu5F2cy17DwKTdfkPrnaopEeqTyqTJ+VjNFvZebuNrF8i8cCvXMH/jqf10O16JqiQ5ohmNJjE3LBCZSgzUPSXJpDdKRWukYOfkCfWEefDZmnpTyMf7t0HPWq3vPXT8WLhHCqSu9Gy3y4JCeI8bEoZbIrNwbNEEiO/FbiBn+cL42tsD2/hhqda5dZtmqYDsxqKsbzq6ZpWnGf1lAomzsmsfusDztX/n+3ZhaWjVGeuKvVp3PtMqrJtVq0LMU6yP0eq9uq2fWy+d2Et72RIs1AMGYO1DsgH2yF9hPJPbLweivNGtW9kqxpa2ME5sSv3zYLf7htlqlmbWbQUZWHq6fX4WvzEm1iQOp4FsPMPqmnKMeikhELIJdnxfd1w5g+nHCXPcIwRSpspF1ANfs1p98+lMTbd81FUU7yAL+i3VzbzSk6kqeSoHHs0xOWcrjjhvG7MCuAyzUmETUDjvC3HRP12U3FeGvbocS9CfesKwyh80g3dZlGai3dUU6qjtZFFQN10Yr4GxLuzBH/1FSu9Ac95m1qXDq5GvuPn8HtC5ooTDgBmp7LLxD0mxBhkjQ86Tav1tHHjL5yv09fq/ztzTNQd+8rAKK7zOKdZvNaejjTp7nEP94xG7sOdcHn9eDhc1rxtkCmSL85/8rVNgaUDmf6vTjTP5hUpl6cNIcEEvJCrh1brajwpcd9ithcxTTctVzrUtavX296mUZWvpTCDetFmIOnpjCUZJ+/9RuL8cg5rYplmNUxtZZDszNkp8xYv349PvzwQwwODKqfbAJeHQET3LYiKURYt1HlObh9QZMz9bBJ7RNlt+85JTombbf/uH8+XrlFW9hrM1FORErfy2gWaSwf6MUh6KjREz3JyKOEAj48sLxF5Kwtvc327dsBAEeOHKEqk1/5v2yyNQsKyVYK7vTpeeP2WZb5ov3HVROpzsuN+dv85d55AKJy5xc3TMNTV05A59pl8e+uRRo1FGdjviDxrZD+gURJ/FgF8I7tQqLntVAGpglqjOinBZoASkL0j2/KSo4VYwKpfUrvIvc89y8bTXWe/L3p+yXp1A8//NCS+bGVMKWHAiu25vWUyHHRaCD/ff1Uye+KUwe6+qhUKMPnVbURrSt0X3b6W85uRH1xlq2mT5FIxNYoVULTBSGy5jLgbJvQ60FYM72v8fELO3DP4lG2KXeXTa5BFmWY9xmUCRILsgKYKtkNLcrOQFaGtkmaFQE1ZLK3mH4fuzDyhoS+T9LobbZBuK/SsFCeG8QH952Nry+V90k0VB2FY/wE8qa5ZFM9raibt8kzsoQu0A4tNHJ11ax60b9vm9+IrIBX9L0m1RXEw3ibTZ9gp0c4VsntIupJBaAvWqE8NAGU9CAXIj0eLVXyHLyPsDBku5MLiNfOrJf8oq0yWr7SiKLk+Z3dcx0zYEoPBZmZco7O+hGZXqgUJIzeFg76k8IzThVkPU/K/2PTAltlXqYlieVoUHrGySMK8Kc75hAFNweywFr/MNmpWC6cspTMzEyEQsYd+oUkTKySj2XLTIKVRBGVnHLB/E2vPL1gQhVWz9E/qRIuJEirQHrfY6pysenRxaLfxsvsyP7rRfJ5q7yCvv3RAwtQbELEQWE4Zq35VaRI29/K8eSAFurlaBNME2q1+xiSEH1LoXmblhVPieRvKs3Bm3fOAZCcp0dP+TxaElgHMqLtxOdTVoiFKQnKcoPwmeCbpzbRl/OFIkUls8doyHqUPvd9S8Wr81efNSJJdhDLNHBf4e85goSamZmZyMrKwlXjC/G9S8ZpvuPfvn52/G9Re3XYHIumuz37lUlJC8jx62P/5ds2X95V0+vwnQvaMc0k03zhvZxA+J4q8zKxvF3e9/GG2Q1J0XhDoZDs/NitMJ8eCpqamgBsN1SGtGFfPKkG+0/04Km3dxLDwNLy/cvGYXFrGd7bcYR4H1qMauutFWHTVpRJVZlYm49/7D5Gfb4RwjJhk2mJthfA490LwLjNvNtJ9kFLPmf7N5fg8qf/ir/tOmr6/S+jDJFtp4XNO3fPRUFWAK0Pva7putxwLoAuTde8cssMDA0BK77/LvG4sFs+e/VkvLntoKby5djxraW6cyPZsTqo5XsbPbcsFvbcrp0e6W1qa2sB7EFeXq4rTFcjkUhcOVw9uwG/2/S5c5Wxsd+74d0r0VCchScuHhv/Nz9WPULMFqH+MCUWJJO1EmGy5DmEMOVq38/v9cjuOuVmGps3KGHV2CVcwPnepWNxsmcAL68/QDzX6+HQVpmLLZ8nTLBbWvSlGXESttNjE9K+lBnw4uuxFR9aJYd0WklOdLVOOomw25fF6gnlueP0J8PjYVFStCEn/6WRsGjGeb/XQ/32tZrejabMBaUXPa2muiCk2QxNL60VuRgjk+cLEMuXmsIQvjytzvA9I5FILGmusT5lia+Hjomn0VqoRXcyskqvhUgEaCrLQSjglQ0rbzbkQAb6nsfKccTORQ/aW/39n+YLrtFWQeHZcnn+pGUvaStXjDiqtz8uby8XvV9SKWoKhZkKo9Gy9LwHYf4sbTdTP0XpeYQ+V1qfW2oBU5RlbzRaJ2BKjwaEqwROoEcc2SXozVQotIfZpjuPNJmWm2DPaS7GnOZi6cmWwZvHmIkVn75z7TJVW/OKPPLqH+3rE5m3OWRjp/TuzIh4JcTqJ7QiR67ROtNMKqySXXzOkkyBn5828zb5Mh3z6REQDvqx+dHFunOk8Bh5/QEKszm7XpVy8A1nIZmv0taTt6z41Y3TUS6TskIrpETNamx5bDHWrmwX1Ts/RJc7ySqciJshzdVkFdLmIbR0qMzX1g6mjEi4Rng9HsXFs3SBmbdR8p9XTyI6ctFiPNQA+RrpDk/cAc/mTm/m/UhCXzliknn35nn2K5MBIB6SVIl/vagjnrhQL3VqbcvEUK4RmOt8KK1ZYXYGOtcuo3p3dvPk5eNxumeA6lw5RV4pt4mbaCrNxrYvTot8eozC52fK0bmLZYtcUrlHbWEIj36pFecJdo+liuGNSv5ghPI9LlF6TJXDOq9rrQjrDhxjxc4faeEkmubB9Fvhuln16DzShdHlYby7/bCma7U+eqLNmfcsT315IjbuO6GpXtJv/b1Lx2H+aHJSdbeT8J+O/VvDe9XbdmkWjGmKvm1+E9qrtEX29Xg4fPLoYvzXX3ejYxgoPABTeqjYs2cP5o4yL3qIVHlSDWQQj9Uu71wtPdfusdeKycy0+kK8v5P3VTL/BprrLHP++RJn7j179mBwcBCDcl7NNqM0wN+7xHj0JiubmtnteCkhSaWSckiitSKMTftPar73W3fNUT3ndJc2fx4l2qvyTFd6ynKD+M4F7VjSZiyyFE3I6pIcnf4CcdNecukcxxFM/MTn3r1Yvl9MrivA9bPq8dTbOwVlAotaS3GTTGJQ62zyo3z+edRn5vRpuvZjZreSllUi2b2Q9iOzF+Zoy7HiG0iDklTmZcYXzKyGV9TFC1jKDyn9FvxY5fV6UV1djYKsAGY1iS0ctMrgczr05fMze1dfOF/66IEFGP/YH0wtXw//ftl4bPvilPqJMR45pxXPvLdL9FuSD23sv1p3eXgyA15CFDgy0kAGnZ2d8baTKjDzNgqOHqVzvqbJn/Ot88bgtVsTeTbuWNCEH3+VLCSTdnEUypVbZbDLj8WK+8wWmJdZNWnQJNApzz169CgOHz6MiMNKD//KdnxzqeT3xMs8ixBBices3SDpJEiNiMzfbuDde+bKRvxR4u7FzagpUI/o19vbq6daRPhdB7P7zkUTq5FjMNgHDW2VuXg1lpOIgzEFWO0daHlHPq8n7o+ZuJ7Dj66cqHmlVQmlxw3EEmpmxyJxnTgZVcJ7e3pMu7/eZsOPRVaIbFK4dyc3184fX5W06MVj9a4mv5gxSJERV64u/FhFO8exg2tnjDC9TLkIgmZC87mXtZfjNkneOaV2ctGkavxuzSxR/ZO+to0d4KtnjcAf75gd/7fb2g4NbKfHJN68cw6KFCZ3/ECQleEVbQfffHZj8rkU96OVp/T+LgahvI+aw6VckdLiR5Zk49ODp6nLIpefeoEN9AykpKh6ZopJtSr9lQ9rqsOpZ6FMgj0zIdVf7j1X5esLRX7jHPIOgKXEXqOZOz12QxsmXo1QLIdSY0k28bjVb8hss62RJTn4lwvasULnqrpWCrICONrVRzwmN+cajB0Qtr+Xb56B12OR3Gy3RrD3dqY/n7QN8f8ejESod0n01Mm2OUSMGY10ecx4aJOn0hAxsFBkpYl/KODDY+e24YFfb5S/v3m3j/Prm86C35so2ePh0FBMlqGpAlN6KGhublY9R80nw8iqedzO1IKOePfiZuw42IXfbzYWUpSmah89sEDkPEzD+eMq8bfOo0nP8Z9XT8I3X/nEUCjU7KA1zb+5uRmRSASBV4+iq79fdznv3TsPAwac5uVa3JT6Avzqo30ATIoYpXJc74TvmasnYi4hrKjZuGk3KTc3F4A5q/X8To/Hxfv5WhQy6lMJ5xVmZ+D1NbMwUkbpMZLTySykizBqj3uhIHRuNGT1QeTnm7fTJOTNu+agt38Ix7v7CP460sih0X8PDEb/K4zcWFNoXv6yd+6eC7/Xg+X/9k7SMZos926FdqrAx4qgOV+uLfFjlSVRFGMsai3F65u+UD1PzxTp7bvmIj8redd53qgS7Dl2RnuBDkD95h3Y0hxbrSxPWltbLW07VsCUHgV+t2YmPByHYNAdseiVGpfeFQp+BXrMQ8aUHprJi54t5n+N5RR4/u+fab5WjuXt5ZjVWIxzxlbgqmf+pnhuXWEInUe6Rb/95mtn4Zzvvyd7Dd9eXlg1DX+J5U/SSgTiTO9m0bl2GQDglx/tpaqDE/D39Xk8dAI1xYSuFOFY5vXqcwAnlhv7rxt3eiLxXSjt16ifGP2P9LGbZUKb833CbWjpf4FAVLZ6vdYM6eGgHwiSo43J0RdbsPF5zWt/wh2N6pi56OymErykJM9cqu3MHy3exdb6lvQEz5CeacfcZlJdAZXSowc5Jfrq6XV47JVPLLmnHFon/7xVIjFxuha5qOmu5pJqiUkBG3x63n33XSxduhT5+fnIzMxEY2MjHnvsMatvawqjysJoKjUnB0iqacNasTrdhhmmaHwZOUE/LppUjaDfqyow3rxrbtJv7VV5qC5Q7+yNpTm4anqdjprKo+U92NXiaO+j1QTDjDb1/PVT0VQaXd0v1ZBIz87uWmvi6rcQPYqFXST8jVxYORNxW5jkRD4h6yrGf1PhTo+euwnNaoT5bKSsXTmGOHFMqpfM306w7qGFePLy8YbK4OJKj/A3Q0WKkDaRuaNKMGVEAVZ0VFCFJNd8v9h/9cqE9++bhzGVKubzarmC+DrY0EJ4XyxS2yV2T5X3Yua3pzEZzAqYt0BnJ5bu9Dz33HO48sorcdFFF+EnP/kJsrOzsWPHDuzfv9/K26Y88YEp9u+RxdlYt+e4yjXkFn/xpBq8usH6bNiWiwhTzLAIkkTDaGzn/EX6uFa9XzfPOc0YeKbUF+L3t83G5v0nDYcVp6EgK6A5cMM9i0ehtSKM219YZ2pd7FYsKvIy4fVwVI7VcdM7DQEG3NxWhzNy+hOfz0rvBLm5LAcb96lHSfR7PcgP+XH4tIzPka67G0fJNyU3Uz4QCO3iEN937AqTHg768fyqaQCADJ8nvpNnF09dOQH1xVmY/69vE4+X52aiuSwHGyQht41g5ZsdiMlJH6X9cV6szYQtMsvnefeeuchTybP08QML4DVxB9dOLHt7+/btw/XXX49Vq1bhySefjP8+d27yyrlbOX36NIaGhuDxeJCdbY7zlh759M3z2nC1zh0DNZtMs7BiYqW0MmemyYTZmNFuzBC2FXmZSaZ58fIdmAnQ3tOKhKRaFR69CtdHDyzQfE3A58GE2nwAQL8BHzApPo91UbRIhAI+7PjWUsX8TFx8ohb9L80KPQ91m3WRaLBLUevujvovDAwYaz+r5zSgIBTAN1+lNw26aFI1/rjlYNLvWbFcTnkhf/yTcND3eRI7VDoulpQBAEvGlOOV9Qd0lVMazsAXJ9WjLGrOVaS2ACD5dzwh7lBE/b3IlK00Vmluu89o2rkAACAASURBVBaPKWpJsYWY3e+s6Md8Sgvauczy9nJk+DxYIAnuY/ZYThOsJz8rgNOnT+PkyTOmzo/twDKl5+mnn0ZXVxfuueceq25hOTt27EB/fz/8fj86OjrUL7CIoN/r2ky5RdkBHD7dZ9s8474lo5CfFdCVgdrozoHwaiVB45Z28+Tl42VXSmm28Z0yzTHTvM2NFGZnYFFrKe5alJwL5uRJ+hwOavhiK+xOJ8wkYekulIse165Xv3dv1KflxAnlVW7eD0SuWvcsHoXXNkSVAdpPs6i1DAtbSvH7zWK/jfPHVSIr4MXspmJ8/0+fJl2nZXHD7Fby3YvH4tsr23Vd+8otM3H4tHmh5eNobCt8VE6KjdXELSTnKo1VtosNitxdNlUhXonibG279jxPf3miai43fqfHS9nROI5TVPzsHi/dMs/RimU+PW+//TYKCgqwZcsWjB07Fj6fDyUlJbjhhhtw8qT2xH4MfUg7wss3zzC1/Bdi291WSyp+chQKeHHRRH2JsEiDrJaB10nztvjvggPhoA9Bv3wXzgsFVMN/KglKLU7LVmD34Pfg8hbkWGw6AER3N3505UTZSGJm4Y8pPb0D7kiSK4TavM1N2zYWY8ek5ZZ5jbh+Vj06TMwnBJBlo8fDYcmYclf6bfm8HmRnKPf1kSXZKCQE3ynKzsCoMutNZdVI7JpS5Okx0I/4iX9ZbsIn8tmvTsaq2eKElk1lqbPaL+VXN07H3YuTo/T+88ox+NGVE5Dh07ZrN7+lFLfOT05HIoQ3AyallNBCItGz+/qZG7HUvK27uxsXXngh7rvvPjzxxBP4+9//joceeggbN27EO++8oygMN23ahNraWoTDCeHS29uLLVu2AADy8/NRU1Mjumb79u3o7o6a80g1z8OHD2PfvmiY3pqaGuTn58ePDQ4OYuPGaPzznJwc1NdHO3NJSQkGBwdx8uRJrFsXtbdvbW0VlXv8+HHs3r0bAFBRUYHiYnE24/Xr1yMSieDgweSVoT179sQTOzU3NydFUjl0+DDWrVuHkpISlJeLM8kfPhKNCta5uxNT6guTyj5w4ADWretCSWWt6PchgfnDnj174pl0ebG5bds2nDlzBhzHob1dvBJ26NChJH+suLiNROLvKBwOY8SIEaLzdu7ciVOnoqvYbW1toihVx44dw2efRaOzVVZWJj3LunXrsGdPcqbxRW2l+N2mz9G5/RN8QZj8nzx5Ert27QIAlJaWAhDvDm3atAldXeQM5vv378ehQ4eIx7q7u9HXF7Uf37t3L6qqxMnpOI6Dx+ORdRbm31NdXV0sRHEyXxw8CCDxzfmusn79elTk+LCko0q0U3DkyJH4aq+UIUGS1B07dqChQRyet7OzM75CPHr06HgkqOdXTcWs7/wZ/YPyg+rGjRux/4Cyv9m6devQ2CgeALq6uvDpp9HV3+LiYlRUJOcb2bFjB3J7v0jqczx8mxFiREYsbczC9s4Qfr7xJE6dFuSA4pJlhJRdu3bFF3NaW1vh84lFK//N5WTE/pPRfpmZGYQwZLVQRpDgyy0pEYf2nlZfiNMnot9l26c70VoxTnT8wIEDOHgw2SQJAHp6erB161YAQEFBQdJxNRnBc/z4ceTliSfXZ2JmWP39AwDEkeWUZMTAwACOUCTB2759e9Jvn332GY4dOwYAGDVqFDIyEsp8sowgs2XLFowalbwzB0S/wciRI5GVlUhb0N3dje3bt8uaK3Z1dWHdunXwer1oa2sjnrN7926cqMsSyYi+vj588knU9Cw3Nxd1dXUAEBvPDoLjPPE2MWbMGHgE/gK8jFhWCRw/dhSFhcnjxrp16/D5oWQlWU5GANHdpZOCHaY2iSnpxo0bZeXs3r17cSQ2ljU2NiIUCuH+ZaPxjVc+wZDAZ+SLL5Kjf23ZsgW9vb1JfQ2ILpjw7yGrSCxbaGXE4/Ny0d5ufB7BoyQjjh8/js1bdsbqR/ZNGhwaxLZt29DUFE1umZcZ/Qanjh/F9oPR9zs0OCi65vTp09ixYwd2fBGVKaRFPo+MTwnfZ6qDvXjuK+MwrSmxy9Bamgnf8T6sW7cOBQUFqK6uxs+umYI9R6P9WygjAHll6Pjx5LFj586dyD2zX3YeIcexY8fisvLYseNEFWAoMoTt27cnjUeFOIWz8rvwxinxgnw46Me06lC8LZWWlqKsTLzb0hNLCEySEcJ5hFRG9McWo9atW4fCwsKkecTWrVvR09OjKCPWrVuHMz1ixVxORpCulZMRAFBVVSWSEUNDQ9iwYQMAIDs7Oz4/5uW0mozo7OwEAJSXlyeNVxs3bsTg4CCCwWBSihiSjODhx3ItWKb0DA0NoaenBw899BDuvfdeAMCcOXMQCASwZs0a/PGPf8T8+fIRWQYGBpImjZFIJD6IDAwMEK+RG2SGhobix4STQB5SubyiIZwoSeskLHdQInD4ciORCPGeg4OD8WuF5fIaO182qVxeuA0MJB+Llj0Uu7f4vkKhRyqXf4ckhVRY33h5gtdh1reZ3VyMJW1l8R0d4TsQvv3zxlWhI7cPR48eRX9/8rMI28vg4GDSM/X392NIxjaA9KzCcvkHJ71Dj8dD/N7C+8bLkUF6PX9qf38/vreoEOPHjxYJK+E7VCJx78Rvcs9anpuJmQ35+NM2+clmX19f0kBLumckIh5upd9GCH/egMI3IF0nLVdzO4xEMDgUa2cROhlBKpf0XdVkBO+LERXoiYmAUjtUKre9Kheh/mg5Ia+y7JGi9G0AdRnBQ+oD/LuJxHd6EmWQvo0wqItSnxKWwc92+GuVvo3as/KofQO5cuV2koeGIrKynWeQMAYK6yK8tqioCMBWeD2c7jGQL3swuXmrthfhbsPX5oknlH19fYKUCuI2QxoDr51Zj+Pd/Vg0Kh8rfvD3pGcV1pX07oXHgeSdEC0yQroKr2ceQSqXOI8YUB8XhOVePKkaWRletOf24cDBLozM9+HLU8VWEHx9eRlNCl8/NDREDJXPP9/Q0CDayrNF347Ub/JCgbgDvJKMIN0DEMj92LVy71CprEi8zvKyQunb8PMBYbXVZERxyIOdx8gyQm6OByR8euTkAN++VeVSJDkohl6ZRtu++/v7kxbijYwpfX19su1Q6R3qiUJpmdJTWFiI7du3Y9GiRaLflyxZgjVr1uCjjz5SVHp8Ph8xA7Hf748fJ13DH5fi8Xjix0grG7TlCuuUHwqIyiV9ML/fj0gkAq8nuQF5vV5iudI6k8r1xH7zyeT18Hqj10qfVSj0hOXyjYd/VlJ9hPVNkJi8mPVtQgEffnDFhPhxv98Pn7cvVk/6coXtxev1ApJPEH0/4ufkV8/Iz5ool79O7psLV0BIx/ly5JBbfQv4/UTnb+E7VCJxTkK4Kz2rmkgJBAKYUZeNn244LXsO355Eir302wjvGTvN55OvFwCUZEe/VYXA7MKojODfu4czR0ZIr5VrL4Qi4+crvQOlchc05qK9NIMYqlutfSuVqyYjeEhtmL8mEZ42uVxinQCUZPkBKCcc9Pl8SY1W6duoPSuP2jeQK1fO5MTj4WRlO4/XmzwGCusikt/xcuXlgNoYyJft9SmPVVI4jouPK6+uGouAT1x2IBCQlXVyY+Cdi5pFu0Okcc7v92NoaIjYHy8eV5JULv8t3DaP4MsK+NTHBWG5Xg+HL42txJ49e5AVDOD/LC5DvSRJOl/ftjIfrp6UgRslSXj5+pCeNy4LPd6kZzUiIwBg8cgsdPUNicqtLYzWvSg7EJOJ5Hcoh8fjARevs7zZt9K3IdVX7VnvnFGCrYe6ie9QaY532aQq/N8/7ZSVA2rzCP6cCEHG6JVptO1b7VmlqL3DQCCAwcFBze9Qj+msZUpPe3s7Pvjgg6Tf4yt8KmH6Wltbk87JyMhQdJiSblkKKSoqiq2GJeP1ehXLlW6x8lwwoQoeD5dkwiGEN/9Y190J4JA4uVp1ddy8jFjnwiJ0dJC3NYsKCwGcQK3M1mV5eTk6OkbidK94VSMQSJh2kO7Nb52TKC4uRnFxMZ7JKMNXn/0HgMQE1evxoKND3jFUutUvJD8/X2QmIKWjowOdkX3AB8eSfABqamoS5gk/F5t3hcNh0Xc9KnEsbG1tRejtEwCiCtVLq6fFA0ZUVFQkTK4k5YZCIfzs+hl445MvkrakASRtz/J8e+UYFGZloKNF3oyGR7r9y/ft9vb2uIO6kMLCwuhW9M+TTdyE/Yg3bYsHCwAnu/0NAH6fsiLV1taGNgD4rXzELlLfysrKUnV+HNkwEq0NySY4PFcumoJxbSfQJsjNYEhGFBaitLQM2HgKOTnZwJHYDleEJCPE0a3kZASPUp3a29uRe6QLeDkaWv7OhU04dCpqDhuXEYTvqlZuS0sLWmSOlZeXR1fqCOUGg0FJuetFx9VkBA9JLoZCIeDYCXAeL4AB0SKMkozw+Xx49NKp+Pk/vSZ7DhD7vn/7SPSbSEZIkMoIOeRM2wDyNwiFQujo6ID/lcPAmeSVTZr2X1Nbk2T+GggEFK/Lzc2VHTPiMkKBjo4O7N9wAIDYjFlJRuTm5iKcmwvs60FRUXL5bW1tyHrnJHA4ZrYl+OZVVVVEGQpAZAoUNSnaIFr0En2TXyXqK002+/mJHtG/3TaPAKJ9ZWz7GODXB1BXQjZ59nq8xL6nNI/Izs6O12n8uOTjLS1yEoI3mdyFiorypOhcyTJCjLCef3sn2STth9fOSfpt5fhKtFWGFf2lojIiKnt/IMlzlJ+fHzXH3dWN/Pw8AOLofFX5mbhuZj0aG+uSyuVlRM6HfwM+F5u1q8mISePGYJLMMdE8QsKtC0fj1oWjZcuVm0cI6ejowEfvRc1z+W6lJiOE10pRkhEej0exXDUZoXStnPkeoCwjQqFQ3CSaFsuUnpUrV+Kpp57Ca6+9hnHjEr3t1VdfBQBMnTrVqlvbhlEHNDUUnexlbq3XZ1SLxjxvVGLSbpdz/9Ix5dhxqAsX6gxiQMOE2mT/BSHCnYqRJdmaHdEvnkSeeJnJzfNG4o+fkH01SLjQx1hTcIk2tWR0GnCLw7XUPCgdoQ1ZHQ91zCUCMzDch3ARxUx+dOUENBRnieTUB/edrSnUeVF2ABNq83HL2e7uV7khP567dgrG18osADoknsz8pjkZPpzqJZuocRynKUDEkjHl6icJePeeearnJIICOIsVaRsYUSxTehYuXIgVK1bg0UcfxdDQEKZOnYp//OMfeOSRR7B8+XLMmGFuFDEr2Lx5czwkn9KKiBZMEyCSPtFcGnWuntNUopjQTW5epzdDt13hhf1eD25fIL/C7CasaDc8ahPzOxY2446F6itErsZtIattrMexY8ewefNm09uN20j49NCer6HwuE+PWxqQ9fDBGHjnczOwOhoUzTddFAvRe6I74SsgjCJGg8/rwUurp2u6ximmj1SOtmk2SmPV6PKoAjJphPJioBpfGluJVzccwIzGIrx660x8ekjeFJqhHacyElg5z7ESS5fOnn/+eaxZswZPPfUUlixZgh/84Ae47bbb8OKLL1p5W9PgHcnMTBholQZflhtE59plGFcjNimRDltymaC/cpayeY4cEYFvSCqiaS5F+ZBWtBuzcSQ5qcbznGhSwjqe1RCdgNQVZiWd94sbpuGXN5o/keId3PWiFobXLSQWS1R2egjHc9SecRguksadhCmCPTiJ0T7NVsDNRWmsqivKQufaZYYTnBfnZOCXN56F3Ew/qgtCmNtcon7RMCcVwk+nwjyHhKUjZGZmJtauXYu1a9daeRvLUHLa0oqWJkw1t9bYJ6Y3FOI7F7QTnZqBqOPonYu07xDwY2wqrKoaHTBpd8PMbDc8Zr/duLJKef5z103B/uM96idSMH+0uk+TU5THVpHzQwF0VOcl+QfwTKoztvopB+/grodPv7kEf+s8isv+319NrpX50Obp4eHFy4aHFxIjUA13eOdsr4qvrFMY/mTsk1uCFWOVHtoqzc97ZKTNOT2f0ZM/0O46u6XtaCU1lgUdwswtO7PXpypyozlnwkGZqFsR8Q4MxwFV+SHiuUbgTQ3mNBWrnDl8SIWtXl75Dfrpkq6NLM7G9AZzTC++d+lYU8oxizzB7uclk6rRUJyNDoOrm7rrkpevu/34vB5kxCJnZVB+V6eIRxvTOFDnyMg7Eqk2TzYyZ4k6eB8g5lXSik5DZ+WjbIPGMFa0ZzeMVesfXoiASf56fCTPoN+LibX5eHMrOdeeHGtXtuO/PtiNrIAz8jM7w5cUfMqtuKHt6IEpPSnKlVNrMaosBy0VzmaGLsgKyK6Guw3SljGvHL5260zZ61Z0VGDmyCI8+eanltUNAFbPacCeo914ef0B2XPMGvhunteI8bX5qC4wXxFWQ23rXi6nh1U8fmEH3t5+KO4cPdmgDbuTjK/Jx/3LRuPyKbXqJztIPBu5y3ZtHlrRgu4+5bxTbkSvT6bZWPU54/ma3PGYDBORW7jVw81nN2JqfSGq8kO4bEotHv/9Nsxtpl+QrczLxN2L5SM1Ws2Dy1tw90vr1U9k6IYpPTahZyxQEvAeD4cp9crhR6P35VTL0kNTaTYOmGTuZBcZ/uhqUl4oWcjWFyf7bfD826XR6INWKz33LB6Fp97eoaj0mEXA57HdtlprG7RrPpyfFcCXxlbaczMZtNpwz2wswsme5BVBjuNw7Uz50M9OE08YOhjLC+ali97WXmXPzpte30an4XPj5ATdPaRznL6x0F2qsf2MLMnGqlnu7dduwe/1xINBpGKb0TPmuWXBI1Vwt4RMQ9Klff7u1llOVyGJm+Y2YO8x+eSFDcXZ+N6l47CQkCcnFRwH0wU1wZ4ufcRKfnrNFKeroAk+umRZOIj1OIGBmDOgmtLj8XB4+665KM/TFrFruNFSHsbjF3Zgebu2ML52QerzZnbzvFAAh0/3mViiu3jj9tlOV4FhA0asG9gMhg53ej26hAMHDmDv3r04cMCElXeblq3tWh33eDjL8xRp5a5Fo/DdSwgZ2ASc01FB7ccihfZ5jbQbNeXLZdZAluBk9Dan6e7uNkfeuIwlY8rx3r3zMKosqvwMxMzb/BSO9zWFIUdz9BRkBXRfa1e0sc8//xxTS4Fjh+lzdNmJ0YUMtcngT6+ZbOwGwxRT5zgugx+v80L6+6/dpNKuTaq2HbbTo8DBgwfjccjLyw2uoNnUmPnbpFDfcZRE5BP1c//jqkn4/abPVc8z0m6smiS9e89c+ByO7EQdstpteXpspKenBwcPHjQubygpzw3iwAl7zFQr8zLjf/PfWG2nx2neuH020RzWbZg6VunA6fGmPDdT/SRGEk63GyvJzfTje5eO0+TTw6AnVdsOU3pcSHFOBgBgglxmZg0Mx4mjHmhe04iiLKya3WB5XYDkSYRRp34rIvfphf5RWOO1mtdvm4UzKo77379snGX+e07u4NAwsiTb0PVazGalfdxpRUIPck8bjyKqs08zScDQwzkdFU5XQRN6xvnhvEioB6b0KNDQ0IChoSF4zFgh19AiS8NBrHtwIXJ1rDAKQ1QLEQ6g1QWZ2HNU3vdlOGJmpDAj7UZuUnDBhCp8uNu8bOuOQDmLG84JCHNyctDQYI9iDUQjJ6lFT1rebt3EwajSc/O8kSjICuCR3242qUbmYldbNnWsiuHGSdTwlQzWYEW7YTiD3X7Jqdp2mNKjQHa2sVU+I+hReIQozS9/d+ss9A24O3O3XVixmmqk3chNki6dXINLJ9foLtdN0ApnN066rMbv9zsqd+wiHPThZM9APEy4Xu5YGE2o7Falxwha2r/TbUaLGNXTr4ejLLADp9sNQx8zRhZh1+EuAMD0kdEovmMqc6mvX9RqPEF4qrYdpvTYjBtMFrIyfMjKcLoW7mA4O80z3IecePjN185Cfgo55MoSm71+e2V7SjkYM5yFRddkMBL87NpE9M7WilxNuRJ3/fNSK6qUMjClxyaYyHY3bllJTOfBnTZohBsWBtyGXXlq7CI76MO0BvU8Y8MZp/qBXffVFamKyQbGMMDKPmhX0m+3klrGeDbT09ODM2fOoKfHuBMvk9XDByPtxm3+LAtiOY2yTUx6SCtyh6NoHhwcMEXeMNyBXYsYZo5VeuAVGLUJld751jCfp1mG0+2GkbqkatthOz0KbN26NR6Sr6Ojw+nqUJHOOwVWUFMQwro9x01d/UjFdiPHhROrceHEalvvSTuBSkdOnDiBrVu3pny7kePamSNw8kw/ptYPj10eLYsYRlq7mTLHrm43HPu320insYphL6nadpjSo4PX18zCwVPatFunxbvbdhDcwtrzx+CKKe4JEDAclFbayU76v4nhRzjox8PntDpdDVeSE9tNbS7NwdYvTjlWDzebt7FxjMFgGIEpPQoUFBRgcHAQXq9X9HtzWQ6aY5nF3Q5bTFMmK8OHKSavOsu1m+EO7RxnOE5r+H6akZGBgoICZyvDcIScoB8bH1mElz7ci4d+s0nTtU7LHC27NnoWdtg4Zg1OtxtG6pKqbYcpPQpUV5tv1mP3hM4TGy3qi1MzvGAqYkW7SSfU5i/DMdlaWW4QY6vzcPfyMaguCztdnbQgFdtPdoZPV72dljnfOm8M/uuvu5FvMNUCw16cbjcMMakkslK17TClJ83xez347ddmoLGUKT2M1GI4mPrx+L0e/Pqms5yuRlrAm0ClehTAVDLlKssNxnMmkSD1ZU25fYaRLGAMX1Knx6cuTOmxGbtEt7DzjKmiT1rFYFgFP4lLxRV4BmO4wPsW5Wam1q4Nx6W+ostgMKyFhay2GSaTGUqU5gYBAAVZ6Zu4Uc3+P5VWuNUoDbMswHbDdgWMMbOxCD+8YjxWjq8yrUxSn9bylWgWSjxsNYWR4rAWbD1sp0eBbdu2YWBgAD6fD01NTYbKYvJ4+GCk3axoL0dFbhAT69LPmZ06kIGKT88bt8/G8e4+cyplMX+4fTZ6+gepzjVT3jBSX+ZqUd7MHas4LG4rN1SGfNnGrleSIR4OoOtpDB4mc9xJKiz7pWrbYUqPAmfOnInHIWcwaDHSbjiOS0uFRwvL2yvwX3/9DNX5IeLxkSWp458WDvoRDtK1AyZvzGE4+vS4ve0Y9+mhOIfjNJbKcHu7YbiXVG07TOlRgOO4+P+NMrE2OpEdW22xf02Kr26mA2a2m+HItIZCdK5d5nQ1bIe1m9RiQUsp/rD5C9PL1fP1jbadP90xG4dP27N7qqeKNM/lYd1GM6kocyaPKMDi1jKnq2EpqfA1UrHtAEzpUaS9vd20sprLcoblRG44Yma7YQwfWLsxB35Xweqx+KkrJ6ie88/nj8Ez73ZaWxEYbzv1xdmoLzapMhaitI/DfHq0k4oy54VV05yuguWkwn5lKrYdgAUySDtay6M5PuaNKnG4JgyGmFQ3N2IwhNCscs4bVYqfXTtFV/np2F84cJg/uhRAYqyiu04dpvQwUh3WhK2H7fSkGSXhINtRYtjOzMYivLP9sNPVYDDSxqcnXWmpCFsyRjHzNkaqw2SW9TClh8FgGObpqyaiu1c5dtJ3LxmL//77HptqxGCkNmzVNwH/LpQUGw/TehgMhgpM6VHg0KFDGBwchNfrRXFxChg8M1zBcGw3GT4vMnxexXMaS3PwwPIWm2qUegzHdmMFdvn0WI2WVd90bzscx+Huxc340thK2XPOHVuJZ//SaV+l0oB0bzepRirJrFRtO7YqPU8//TSuu+46ZGVl4fTp03beWhf79++Ph+RLpY/KcBbWbhh6SJd288DyFtQVksONMyjQMfNJl7ajxI1zRioef3B5C76+dLRNtUkPhkO7YVhDqrYd25Seffv24c4770RFRQVOnDhh120ZDAaDYSPXzBjh6P2ZT497sXIl2+PhEGAmbowUpjIvEwBQnZ/pcE3SF9uUnhtuuAGzZs1CQUEBXnzxRbtua4ja2loMDQ3B42FB7hj0sHbD0ANrNwwA8MUm7l4NE3jWdhh6YO3GXUypL8Qbt89OiQTcqdp2bFF6fvazn+Gtt97C5s2bcf/999txS1PIy8tzugqMFIS1G4YeWLsxh1T36Vk5vgoHT/Zi6Zhy6mtc33ZS9FukO65vN8OQVFB4gNRtO5araAcPHsSaNWuwdu1aVFVVWX07BoPBYDBcxy3zRmJCbb7qeQGfB7fOb4Tfm1orqIowU0MGg+ECLN/pufHGG9Hc3IzVq1drum7Tpk2ora1FOJxIYNbb24stW7YAAPLz81FTUyO6Zvv27eju7gYAdHR0iI4dPnwY+/btAwDU1NQgPz8x+AwODmLjxo0AgJycHNTX14uu3bVrF06ePAkAaG1thc+XeG3Hjx/H7t27AQAVFRVJDl3r169HJBJBZmYmmpqaRMf27NmDo0ePAgCam5sRDAbjx06fPo0dO3YAAEpKSlBeLl7127x5c9yJrKVFHBHrwIEDOHjwIACgoaEB2dmJlYOenh5s3boVAFBQUIDq6mrRtdu2bcOZM2fAcVxSxt1Dhw5h//79AKJbm0JNf2BgAJs2bQIAhMNhjBghtuvfuXMnTp06BeD/t3fvQVGddx/AvwvL7nITkEURlGhFILIYM2kMvlNvUdTWdIiZRtvpNM2b10srprFvjUYTK0RRJ2n+ME41zXTyOiMk6VDbzjDSRhOWzjQxk6mmFB3T8UaRSXAREGEF2WV/7x92T/bOemTZC9/PDON4nuc8+5w9Xx722XMDTCYT4uO/vtNXT08P2traAAC5ubkwGo1u6zY3NwMAkpKSMGvWLLeytrY29PT0AACKioqg1+uVslu3buHq1asAgMmTJyM7O9tt3fPnz8Nut0Ov16OoqMit7Msvv0RnZycAID8/H8nJyUrZ7du3cfHiRQBAZmam12T+X//6FwYHBxEfHw+TyeRWZrFY8NVXXwEApk+fjrS0NKVsaGgIFy5cAACkpaVh+vTpbutevnxZuQFISUmJ22Hlrq4utLe3AwCmTp2KzMxMpczhxq1W4QAAE6pJREFUcKClpQUAkJKSgpkzZ7q129raqlxn9+CDD0Kn0yllvb29aG1tBQBMmTIFkya5P/T23LlzGB4ehsFgQGFhIXxpbm7GrFmzkJT09cXtVqsVly5dAgBkZWUhJyfHbZ0vvvgCd+7cgVarRXFxsVtZR0cHrl+/DgCYMWMGxwhwjNi1KBNdt4dx8eJF5Zoep0gZI/53eSH+57YND716ElarFc3NzeNmjOi33u2T5wGf9vZ2dHV1AQDHCI4R/Bzhgp8j7go0Rjh/T+9FSCc9x48fR319PT7//PMRn1ztyW63QzyuRBUR2Gw2pdzXOs5yTw6HQylzOBxe5b7adfbBZrMp5Z59cm13eNj7OSU2mw0igoSEBK+y4eHh+2rX37a6tuu5ra7voa92ne+hr/0VbLtjsW98tRsoL/7eQ7vd7vOc1ED7Jph2bTabz7JA7TrXHaldX4J9D32t79onTyNt69DQEBwOh9sfH1+vrfY99PUeBbtvIiWHwY4RWq1W+d1zfiDiGAGlrUD75qEsLQBt1IwRDoeM6hjh/Fs1NDQUkWOEczs8t2Y0xtnxNEbwcwQ/R4zUrnPdkdr15V7GCOeY4/x7FarPESO9h/cqZJOe/v5+VFRU4Pnnn0dOTg5u3rwJ4O7GAXe/2UhISHCb+bp1TKv1+oXRaDTKL73rtySu6/gaFAAgLi5OKfMVTl/tnj9/XvnFdZZ79sm1XV87LCEhQflA4yk+Pv6+2nX911+7ntvqui2+2nW+h74Gq2DbHYt946vdQHnx9x661nEVaN+M1O6dO3cA+B40ArXr7FOg/t7vezjStnoaaVt1Oh2Gh4f9ru98TTX7xuFw3PPvTSTmMNgxYnBwEM3NzUhISFC+YeYYAaWtYPeNxuN4QiSOEXFxd8t9lakZI3z9rfJ+zfCNEXF+vvS8n/cwGsaIVL0WGck6r3Yj5XOEcwLgayIQy2NEoHYjZYxISEhQnoNzL+061w3U7miMEc4xx/n3KlSfI0Z6D++VRtRMlYLQ2trqdWjSU3l5Of70pz/B4XAohyydUlNTw35XiObmZredShQM5uau6S+dAAC0HlgV5p5EB+ZmdGyqPYOGlg6c3vE4pqRF1q1fe/9zetuSwiz833/PG7V2Iz07a946jc9au3Gx+tuxda3SCOzDDmg0mnu6E99YivTcUOSKhOyomTuE7EhPdnY2zGaz1/IDBw7gr3/9K/785z97nXMZaSZMmAC73e7zmwEif5gbUoO5IbWYncikjfAJHnNDakVrdkLWW4PBgMWLF3stP3r0KOLj432WRZqRjlQR+cLckBrMDakV8dmJzAMd417E54YiVrRmJ7qmaEQUNbYsm4Wi7NRwd4PGGc9reiJJou7u+exrH502Qk0iIhptYz7pOXr0KI4ePTrWL0tEY2zLsoKRKxGNMs9bVkcSnTaO17gREYVJZJ9wSkRERFFty7JZmGFMhjZCL+gnovGBp7cFcOXKFeVCLc8HjRH5w9yQGswNqRXp2fmvmUaYty4OdzfIQ6TnhiJXtGaHk54A+vr6lFvyEQWLuSE1mJvREcnX9IQKs0NqMDekVrRmh6e3ERFRzIjka3qIiCh8eKQnAJPJFO4uUBRibkgN5mZ0jacjPswOqcHckFrRmh1OegKIj48PdxcoCjE3pAZzM7rG0xEfZofUYG5IrWjNDk9vIyIiIiKimMZJDxERERERxTSe3hZAT08PHA4H4uLikJGREe7uUJRgbkgN5mZ0jadrepgdUoO5IbWiNTuc9ATQ1tam3JIvmnYqhRdzQ2owN6NrPF3Tw+yQGswNqRWt2eHpbUREREREFNN4pCeA3Nxc5fAdUbCYG1KDuSG1mB1Sg7khtaI1O5z0BGA0GsPdBYpCzA2pwdyMrvF0TQ+zQ2owN6RWtGYnuqZoRERERERE94iTHiIiIiIiimmc9BARERERUUzjNT0BNDc3K7fke+ihh8LdHYoSzA2pwdyQWswOqcHckFrRmh0e6SEiIiIiopjGIz0BJCUlwW63Q6vl20TBY25IDeZmdDxeNBkNLR1INYyf95HZITWYG1IrWrOjEZGwP7ba4XCgr6/PbVlqamrU3f+biIjCb9ghiI8bP7esJiIab9TMHTirICKimMIJDxEReeKkh4iIiIiIYhonPUREREREFNOi6wqkMdbW1qZcqJWXlxfu7lCUYG5IDeaG1GJ2SA3mhtSK1uzwSE8APT096O7uRk9PT7i7QlGEuSE1mBtSi9khNZgbUitas8NJDxERERERxTTesjqAO3fuQESg0Wig1+vD2heKHswNqcHckFrMDqnB3JBakZCdiLpldWNjI5577jkUFRUhOTkZubm5KC8vx5kzZ0L1kqNOr9fDYDBwMKB7wtyQGswNqcXskBrMDakVrdkJ2aTnyJEjaG1txQsvvICGhgYcPHgQFosFpaWlaGxsDNXLEhERERERuQnZ6W0WiwWTJk1yW9bf34/8/HyYTCZ8+OGHyvJIPb2NiIiIiIgii5q5Q8huWe054QGAlJQUzJ49G9euXXNb7mve5XA4QtW1oLm+mampqWHsCUUT5obUYG5ILWaH1GBuSK1IyI6vecJIx3HG9Dk9vb29OHv2LB5//HG35b46abVax6pbQfGcTRIFg7khNZgbUovZITWYG1IrkrIz0qRnTM8fq6iogNVqxcsvvzyWL0tEREREROPYmB3p2bVrF2pra3Ho0CE88sgjY/WyREREREQ0zo3JkZ6qqirs3bsX1dXV2Lx581i8JBEREREREYAxeDhpVVUVKisrUVlZid27d/us43A4vC5I0mg00Gg0oewaERERERFFGRHxuoYnLi4u4N3bQjrp2bNnD375y1/ilVdewZ49e0L1MkRERERERH6FbNLzxhtvYOvWrVi5cqXPIzylpaWheFkiIiIiIiI3Ibump76+HgDwl7/8BfPnz/f6iWT9/f3YsmULcnJyYDAYMHfuXLz//vvh7haFWF9fH7Zt24bly5cjKysLGo0GlZWVPuuePXsWy5YtQ0pKCtLT0/HUU0/hypUrPuseOnQIRUVF0Ov1mDFjBqqqqmCz2bzqWSwWPPvsszAajUhKSsL8+fPx0UcfjeYm0ihrbGzEc889h6KiIiQnJyM3Nxfl5eU4c+aMV11mhlz94x//wKpVq5CXl4fExERMnDgR8+fPR01NjVddZocC+e1vfwuNRoOUlBSvMmaHnJqampRLRzx/Pv30U7e6H374IebPn4+kpCQYjUY8++yzsFgsXm3abDZUVVVh+vTp0Ov1KCoqwqFDh3y+/pUrV/DUU08hPT0dKSkpKCsrw9mzZ0OyrX4JeSkrK5P09HR56623pLGxUdatWycApLa2NtxdoxC6evWqpKWlycKFC5V9vnv3bq96Fy5ckNTUVFmwYIGcOHFCjh8/LsXFxZKTkyMWi8Wt7t69e0Wj0ciOHTvEbDbLa6+9JjqdTtavX+9Wb3BwUEwmk0ydOlVqamrk5MmTUl5eLlqtVpqamkK52XQfvve978mSJUvk8OHD0tTUJHV1dVJaWiparVY++ugjpR4zQ57MZrNs3LhRjh07Jo2NjVJfXy/f//73BYDs2bNHqcfsUCDt7e2SlpYmOTk5kpyc7FbG7JArs9ksAGTfvn1y+vRpt5++vj6lXlNTk2i1WikvL5eTJ09KTU2N5ObmislkksHBQbc2161bJ3q9Xl577TUxm83y0ksviUajkerqard6FotFcnJypLi4WI4fPy4nTpyQb33rW5KamipffPHFmGy/yN2LgMjFiRMnBIC8++67bsvLysokJydH7HZ7mHpGoeZwOMThcIiISGdnp99Jz9NPPy1Go1F6e3uVZa2trZKQkCDbtm1Tlt24cUMMBoNs2LDBbf3q6mrRaDRy/vx5Zdmvf/1rASCffPKJssxms8ns2bNl3rx5o7WJNMquX7/utayvr08mT54sS5cuVZYxMxSsxx57TKZNm6b8n9mhQJ544gn57ne/Kz/+8Y+9Jj3MDrlyTnrq6uoC1nv00Udl9uzZYrPZlGUff/yxAJDDhw8ry86dOycajUb27dvntv769eslMTFRurq6lGUvvviiJCQkSGtrq7Kst7dXjEajrFmz5n43LWic9HhYt26dpKSkuO1sEZF3331XAMjHH38cpp7RWPI36bHZbJKYmCgbN270Wmf58uUya9Ys5f81NTUCQE6fPu1W78svvxQAbt+ELFu2TAoLC73a3LdvnwCQ9vb2+9wiGktLliyRgoICEWFm6N6sWrVKZsyYISLMDgV27NgxSU1NlWvXrnlNepgd8hTMpKe9vV0AyP79+73KCgoKpKysTPn/3r17BYB89dVXbvU++eQTr7Oj8vPzZcWKFV5tbtiwQRITE70+c4fKmDynJ5qcO3cODz74ILRa9+e2zpkzRymn8evy5csYGBhQ8uBqzpw5uHTpEgYHBwF8nZWSkhK3elOmTIHRaHTL0rlz5/y2CQDnz58ftW2g0Ort7cXZs2dRXFwMgJmhwBwOB+x2Ozo7O3H48GF88MEH2L59OwBmh/yzWCzYsmULDhw4gKlTp3qVMzvkT0VFBbRaLSZMmIAVK1bgb3/7m1Lm3Nf+9rFnFrKyspCdne1Vz7WtgYEBXL582W+bAwMDfq8zG22c9Hjo6urCxIkTvZY7l3V1dY11lyiCOPe/v4yICHp6epS6er0eycnJPuu6Zom5ix0VFRWwWq14+eWXATAzFNimTZuQkJCASZMm4ec//znefPNNbNy4EQCzQ/5t2rQJhYWF+OlPf+qznNkhT2lpaXjhhRfwm9/8BmazGQcPHsS1a9ewePFifPDBBwBGzk0wWUhOToZOp1Pq9vT0QEQiIjfakauMP4EeisoHphIQfEbuJUvMXfTbtWsXamtrcejQITzyyCNuZcwM+bJz506sW7cOFosF9fX12Lx5M6xWK7Zu3arUYXbI1fHjx1FfX4/PP/98xH3F7JDTww8/jIcfflj5/4IFC7B69WqUlJRg27ZtWLFihVLmbz/eTxYiITc80uMhMzPT54yzu7sbgO/ZL40fmZmZAHx/K9Hd3Q2NRoP09HSl7uDgIG7fvu2zrmuWmLvoV1VVhb1796K6uhqbN29WljMzFEheXh6++c1v4jvf+Q6OHDmCDRs2YMeOHejs7GR2yEt/fz8qKirw/PPPIycnBzdv3sTNmzcxNDQEALh58yasViuzQ0FJT0/HE088gX/+858YGBgYMTfBZMFqtWJoaEipm5GRAY1GExG54aTHQ0lJCS5cuAC73e62vKWlBQBgMpnC0S2KEDNnzkRiYqKSB1ctLS3Iz8+HwWAA8PX50Z51Ozo6cOPGDbcslZSU+G0TYO4iXVVVFSorK1FZWYmdO3e6lTEzdC/mzZsHu92OK1euMDvk5caNG7h+/TreeOMNZGRkKD/vvfcerFYrMjIy8MMf/pDZoaCJCIC7R1uc+8/fPvbMQmdnJzo6OrzqAV9nITExEfn5+X7bTExMxDe+8Y3R2ZiRjMntEqJIQ0ODAJD333/fbfnKlSt5y+pxJNAtq9esWSOTJk2SW7duKcv+/e9/i06nk+3btyvLurq6xGAwyE9+8hO39ffv3+91G9DDhw8LAPn000+VZTabTYqLi+Wxxx4bxS2j0fbqq68KAHnllVf81mFmKFg/+tGPJC4uTnmOCrNDrgYGBsRsNnv9rFixQgwGg5jNZmlpaRERZodG1t3dLbm5uTJ37lxl2bx588RkMrl93j19+rQAkCNHjijLnLesPnDggFubGzdu9Lpl9bZt20Sn00lbW5uy7NatW5KVlSVr164Nxab5xEmPD2VlZZKRkSFvv/22NDY2yvr16wWA1NTUhLtrFGINDQ1SV1cn77zzjgCQp59+Wurq6qSurk6sVquI3H3gW0pKiixcuFAaGhrkD3/4g5hMpoAPfNu5c6c0NTXJ66+/Lnq93ucD34qLi2XatGlSW1srp06dktWrV/OBbxHuV7/6lQCQlStXej3szfX2r8wMeVq/fr384he/kN/97nfS1NQkv//972Xt2rUCQF588UWlHrNDwfD1nB5mh1z94Ac/kO3bt0tdXZ2YzWZ5++23pbCwULRarZw6dUqpZzabRavVyurVq+XUqVNSW1sr06ZNC/hw0tdff12amppk586dfh9OOmXKFCkpKZE//vGP0tDQIAsXLpTU1FS5cOHCmGy/CCc9PvX19cnPfvYzyc7OFp1OJ3PmzJH33nsv3N2iMfDAAw8IAJ8/V69eVer9/e9/l6VLl0pSUpJMmDBBnnzySbl06ZLPNg8ePCgFBQWi0+kkLy9Pdu/eLUNDQ171Ojo65JlnnpGJEyeKwWCQ0tJSt4GIIs+iRYv85sXzQDozQ67eeecdWbBggRiNRtFqtZKeni6LFi2SY8eOedVldmgkviY9IswOfW3//v0yd+5cSUtLk/j4eMnKypLVq1fLZ5995lX35MmTUlpaKgaDQSZOnCjPPPOMz4dxDw0Nye7duyUvL090Op0UFBTIm2++6fP1L126JE8++aRMmDBBkpKSZOnSpXLmzJlR385ANCL/OZmPiIiIiIgoBvFGBkREREREFNM46SEiIiIiopjGSQ8REREREcU0TnqIiIiIiCimcdJDREREREQxjZMeIiIiIiKKaZz0EBERERFRTOOkh4iIiIiIYhonPUREREREFNM46SEiIiIiopjGSQ8REREREcU0TnqIiIiIiCim/T+vwYtok0D+uAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d91740e320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "zs = [sense() for i in range(5000)]\n",
    "plt.plot(zs, lw=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That looks like I would expect. The signal is centered around 10. A standard deviation of 2 means that 68% of the measurements will be within $\\pm$ 2 of 10, and 99% will be within $\\pm$ 6 of 10, and that looks like what is happening. \n",
    "\n",
    "Now let's look at distribution generated with the Student's $t$-distribution. I will not go into the math, but just give you the source code for it and then plot a distribution using it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import math\n",
    "\n",
    "def rand_student_t(df, mu=0, std=1):\n",
    "    \"\"\"return random number distributed by Student's t \n",
    "    distribution with `df` degrees of freedom with the \n",
    "    specified mean and standard deviation.\n",
    "    \"\"\"\n",
    "    x = random.gauss(0, std)\n",
    "    y = 2.0*random.gammavariate(0.5*df, 2.0)\n",
    "    return x / (math.sqrt(y / df)) + mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d9173e6c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sense_t():\n",
    "    return 10 + rand_student_t(7)*2\n",
    "\n",
    "zs = [sense_t() for i in range(5000)]\n",
    "plt.plot(zs, lw=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see from the plot that while the output is similar to the normal distribution there are outliers that go far more than 3 standard deviations from the mean (7 to 13). \n",
    "\n",
    "It is unlikely that the Student's $t$-distribution is an accurate model of how your sensor (say, a GPS or Doppler) performs, and this is not a book on how to model physical systems. However, it does produce reasonable data to test your filter's performance when presented with real world noise. We will be using distributions like these throughout the rest of the book in our simulations and tests. \n",
    "\n",
    "This is not an idle concern. The Kalman filter equations assume the noise is normally distributed, and perform sub-optimally if this is not true. Designers for mission critical filters, such as the filters on spacecraft, need to master a lot of theory and empirical knowledge about the performance of the sensors on their spacecraft. For example, a presentation I saw on a NASA mission stated that while theory states that they should use 3 standard deviations to distinguish noise from valid measurements in practice they had to use 5 to 6 standard deviations. This was something they determined by experiments.\n",
    "\n",
    "The code for rand_student_t is included in `filterpy.stats`. You may use it with\n",
    "\n",
    "```python\n",
    "from filterpy.stats import rand_student_t\n",
    "```\n",
    "\n",
    "While I'll not cover it here, statistics has defined ways of describing the shape of a probability distribution by how it varies from an exponential distribution. The normal distribution is shaped symmetrically around the mean - like a bell curve. However, a probability distribution can be asymmetrical around the mean. The measure of this is called [*skew*](https://en.wikipedia.org/wiki/Skewness). The tails can be shortened, fatter, thinner, or otherwise shaped differently from an exponential distribution. The measure of this is called [*kurtosis*](https://en.wikipedia.org/wiki/Kurtosis). the `scipy.stats` module contains the function `describe` which computes these statistics, among others."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DescribeResult(nobs=5000, minmax=(1.888855071015895, 19.03723274712268), mean=10.01034378048552, variance=2.7776404133106123, skewness=0.009548424333982227, kurtosis=1.4807836826747778)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy\n",
    "scipy.stats.describe(zs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's examine two normal populations, one small, one large:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DescribeResult(nobs=10, minmax=(-1.8942931152842175, 0.49750728125905835), mean=-0.10563915941786776, variance=0.4841165908890319, skewness=-1.8464582995970673, kurtosis=2.5452896197893757)\n",
      "\n",
      "DescribeResult(nobs=300000, minmax=(-4.772620736872989, 4.446895068081072), mean=-0.0006837046884366415, variance=0.9995353806594786, skewness=0.002331471754136653, kurtosis=0.007185223820032061)\n"
     ]
    }
   ],
   "source": [
    "print(scipy.stats.describe(np.random.randn(10)))\n",
    "print()\n",
    "print(scipy.stats.describe(np.random.randn(300000)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The small sample has very non-zero skew and kurtosis because the small number of samples is not well distributed around the mean of 0. You can see this also by comparing the computed mean and variance with the theoretical mean of 0 and variance 1. In comparison the large sample's mean and variance are very close to the theoretical values, and both the skew and kurtosis are near zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Product of Gaussians (Optional)\n",
    "\n",
    "It is not important to read this section. Here I derive the equations for the product of two Gaussians.\n",
    "\n",
    "You can find this result by multiplying the equation for two Gaussians together and combining terms. The algebra gets messy. I will derive it using Bayes theorem. We can state the problem as: let the prior be $N(\\bar\\mu, \\bar\\sigma^2)$, and measurement be $z \\propto N(z, \\sigma_z^2)$. What is the posterior  x given the measurement z?\n",
    "\n",
    "Write the posterior as $p(x \\mid z)$. Now we can use Bayes Theorem to state\n",
    "\n",
    "$$p(x \\mid z) = \\frac{p(z \\mid x)p(x)}{p(z)}$$\n",
    "\n",
    "$p(z)$ is a normalizing constant, so we can create a proportinality\n",
    "\n",
    "$$p(x \\mid z) \\propto p(z|x)p(x)$$\n",
    "\n",
    "Now we subtitute in the equations for the Gaussians, which are\n",
    "\n",
    "$$p(z \\mid x) = \\frac{1}{\\sqrt{2\\pi\\sigma_z^2}}\\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}\\Big]$$\n",
    "\n",
    "$$p(x) = \\frac{1}{\\sqrt{2\\pi\\bar\\sigma^2}}\\exp \\Big[-\\frac{(x-\\bar\\mu)^2}{2\\bar\\sigma^2}\\Big]$$\n",
    "\n",
    "We can drop the leading terms, as they are constants, giving us\n",
    "\n",
    "$$\\begin{aligned}\n",
    "p(x \\mid z) &\\propto \\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}\\Big]\\exp \\Big[-\\frac{(x-\\bar\\mu)^2}{2\\bar\\sigma^2}\\Big]\\\\\n",
    "&\\propto \\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}-\\frac{(x-\\bar\\mu)^2}{2\\bar\\sigma^2}\\Big] \\\\\n",
    "&\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\bar\\sigma^2}[\\bar\\sigma^2(z-x)^2-\\sigma_z^2(x-\\bar\\mu)^2]\\Big]\n",
    "\\end{aligned}$$\n",
    "\n",
    "Now we multiply out the squared terms and group in terms of the posterior $x$.\n",
    "\n",
    "$$\\begin{aligned}\n",
    "p(x \\mid z) &\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\bar\\sigma^2}[\\bar\\sigma^2(z^2 -2xz + x^2) + \\sigma_z^2(x^2 - 2x\\bar\\mu+\\bar\\mu^2)]\\Big ] \\\\\n",
    "&\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\bar\\sigma^2}[x^2(\\bar\\sigma^2+\\sigma_z^2)-2x(\\sigma_z^2\\bar\\mu + \\bar\\sigma^2z) + (\\bar\\sigma^2z^2+\\sigma_z^2\\bar\\mu^2)]\\Big ]\n",
    "\\end{aligned}$$\n",
    "\n",
    "The last parentheses do not contain the posterior $x$, so it can be treated as a constant and discarded.\n",
    "\n",
    "$$p(x \\mid z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{x^2(\\bar\\sigma^2+\\sigma_z^2)-2x(\\sigma_z^2\\bar\\mu + \\bar\\sigma^2z)}{\\sigma_z^2\\bar\\sigma^2}\\Big ]\n",
    "$$\n",
    "\n",
    "Divide numerator and denominator by $\\bar\\sigma^2+\\sigma_z^2$ to get\n",
    "\n",
    "$$p(x \\mid z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{x^2-2x(\\frac{\\sigma_z^2\\bar\\mu + \\bar\\sigma^2z}{\\bar\\sigma^2+\\sigma_z^2})}{\\frac{\\sigma_z^2\\bar\\sigma^2}{\\bar\\sigma^2+\\sigma_z^2}}\\Big ]\n",
    "$$\n",
    "\n",
    "Proportionality allows us create or delete constants at will, so we can factor this into\n",
    "\n",
    "$$p(x \\mid z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{(x-\\frac{\\sigma_z^2\\bar\\mu + \\bar\\sigma^2z}{\\bar\\sigma^2+\\sigma_z^2})^2}{\\frac{\\sigma_z^2\\bar\\sigma^2}{\\bar\\sigma^2+\\sigma_z^2}}\\Big ]\n",
    "$$\n",
    "\n",
    "A Gaussian is\n",
    "\n",
    "$$N(\\mu,\\, \\sigma^2) \\propto \\exp\\Big [-\\frac{1}{2}\\frac{(x - \\mu)^2}{\\sigma^2}\\Big ]$$\n",
    "\n",
    "So we can see that $p(x \\mid z)$ has a mean of\n",
    "\n",
    "$$\\mu_\\mathtt{posterior} = \\frac{\\sigma_z^2\\bar\\mu + \\bar\\sigma^2z}{\\bar\\sigma^2+\\sigma_z^2}$$\n",
    "\n",
    "and a variance of\n",
    "$$\n",
    "\\sigma_\\mathtt{posterior} = \\frac{\\sigma_z^2\\bar\\sigma^2}{\\bar\\sigma^2+\\sigma_z^2}\n",
    "$$\n",
    "\n",
    "I've dropped the constants, and so the result is not a normal, but proportional to one. Bayes theorem normalizes with the $p(z)$ divisor, ensuring that the result is normal. We normalize in the update step of our filters, ensuring the filter estimate is Gaussian.\n",
    "\n",
    "$$\\mathcal N_1 = \\| \\mathcal N_2\\cdot \\mathcal N_3\\|$$"
   ]
  },
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   "source": [
    "## Sum of Gaussians (Optional)\n",
    "\n",
    "Likewise, this section is not important to read. Here I derive the equations for the sum of two Gaussians.\n",
    "\n",
    "The sum of two Gaussians is given by\n",
    "\n",
    "$$\\begin{gathered}\\mu = \\mu_1 + \\mu_2 \\\\\n",
    "\\sigma^2 = \\sigma^2_1 + \\sigma^2_2\n",
    "\\end{gathered}$$\n",
    "\n",
    "There are several proofs for this. I will use convolution since we used convolution in the previous chapter for the histograms of probabilities. \n",
    "\n",
    "To find the density function of the sum of two Gaussian random variables we sum the density functions of each. They are nonlinear, continuous functions, so we need to compute the sum with an integral. If the random variables $p$ and $z$ (e.g. prior and measurement) are independent we can compute this with\n",
    "\n",
    "$p(x) = \\int\\limits_{-\\infty}^\\infty f_p(x-z)f_z(z)\\, dx$\n",
    "\n",
    "This is the equation for a convolution. Now we just do some math:\n",
    "\n",
    "\n",
    "$p(x) = \\int\\limits_{-\\infty}^\\infty f_2(x-x_1)f_1(x_1)\\, dx$\n",
    "\n",
    "$=  \\int\\limits_{-\\infty}^\\infty \n",
    "\\frac{1}{\\sqrt{2\\pi}\\sigma_z}\\exp\\left[-\\frac{(x - z - \\mu_z)^2}{2\\sigma^2_z}\\right]\n",
    "\\frac{1}{\\sqrt{2\\pi}\\sigma_p}\\exp\\left[-\\frac{(x - \\mu_p)^2}{2\\sigma^2_p}\\right] \\, dx$\n",
    "\n",
    "$=  \\int\\limits_{-\\infty}^\\infty\n",
    "\\frac{1}{\\sqrt{2\\pi}\\sqrt{\\sigma_p^2 + \\sigma_z^2}} \\exp\\left[ -\\frac{(x - (\\mu_p + \\mu_z)))^2}{2(\\sigma_z^2+\\sigma_p^2)}\\right]\n",
    "\\frac{1}{\\sqrt{2\\pi}\\frac{\\sigma_p\\sigma_z}{\\sqrt{\\sigma_p^2 + \\sigma_z^2}}} \\exp\\left[ -\\frac{(x - \\frac{\\sigma_p^2(x-\\mu_z) + \\sigma_z^2\\mu_p}{}))^2}{2\\left(\\frac{\\sigma_p\\sigma_x}{\\sqrt{\\sigma_z^2+\\sigma_p^2}}\\right)^2}\\right] \\, dx$\n",
    "\n",
    "$= \\frac{1}{\\sqrt{2\\pi}\\sqrt{\\sigma_p^2 + \\sigma_z^2}} \\exp\\left[ -\\frac{(x - (\\mu_p + \\mu_z)))^2}{2(\\sigma_z^2+\\sigma_p^2)}\\right] \\int\\limits_{-\\infty}^\\infty\n",
    "\\frac{1}{\\sqrt{2\\pi}\\frac{\\sigma_p\\sigma_z}{\\sqrt{\\sigma_p^2 + \\sigma_z^2}}} \\exp\\left[ -\\frac{(x - \\frac{\\sigma_p^2(x-\\mu_z) + \\sigma_z^2\\mu_p}{}))^2}{2\\left(\\frac{\\sigma_p\\sigma_x}{\\sqrt{\\sigma_z^2+\\sigma_p^2}}\\right)^2}\\right] \\, dx$\n",
    "\n",
    "The expression inside the integral is a normal distribution. The sum of a normal distribution is one, hence the integral is one. This gives us\n",
    "\n",
    "$$p(x) = \\frac{1}{\\sqrt{2\\pi}\\sqrt{\\sigma_p^2 + \\sigma_z^2}} \\exp\\left[ -\\frac{(x - (\\mu_p + \\mu_z)))^2}{2(\\sigma_z^2+\\sigma_p^2)}\\right]$$\n",
    "\n",
    "This is in the form of a normal, where\n",
    "\n",
    "$$\\begin{gathered}\\mu_x = \\mu_p + \\mu_z \\\\\n",
    "\\sigma_x^2 = \\sigma_z^2+\\sigma_p^2\\, \\square\\end{gathered}$$"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary and Key Points\n",
    "\n",
    "This chapter is a poor introduction to statistics in general. I've only covered the concepts that  needed to use Gaussians in the remainder of the book, no more. What I've covered will not get you very far if you intend to read the Kalman filter literature. If this is a new topic to you I suggest reading a statistics textbook. I've always liked the Schaum series for self study, and Alan Downey's *Think Stats* [5] is also very good and freely available online. \n",
    "\n",
    "The following points **must** be understood by you before we continue:\n",
    "\n",
    "* Normals express a continuous probability distribution\n",
    "* They are completely described by two parameters: the mean ($\\mu$) and variance ($\\sigma^2$)\n",
    "* $\\mu$ is the average of all possible values\n",
    "* The variance $\\sigma^2$ represents how much our measurements vary from the mean\n",
    "* The standard deviation ($\\sigma$) is the square root of the variance ($\\sigma^2$)\n",
    "* Many things in nature approximate a normal distribution, but the math is not perfect.\n",
    "* In filtering problems computing $p(x\\mid z)$ is nearly impossible, but computing $p(z\\mid x)$ is straightforward. Bayes' lets us compute the former from the latter. \n",
    "\n",
    "The next several chapters will be using Gaussians with Bayes' theorem to help perform filtering. As noted in the last section, sometimes Gaussians do not describe the world very well. Latter parts of the book are dedicated to filters which work even when the noise or system's behavior is very non-Gaussian. "
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[1] https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/Supporting_Notebooks/Computing_and_plotting_PDFs.ipynb\n",
    "\n",
    "[2] http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html\n",
    "\n",
    "[3] http://docs.scipy.org/doc/scipy/reference/tutorial/stats.html\n",
    "\n",
    "[4] Huber, Peter J. *Robust Statistical Procedures*, Second Edition. Society for Industrial and Applied Mathematics, 1996.\n",
    "\n",
    "[5] Downey, Alan. *Think Stats*, Second Edition. O'Reilly Media.\n",
    "\n",
    "https://github.com/AllenDowney/ThinkStats2\n",
    "\n",
    "http://greenteapress.com/thinkstats/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Useful Wikipedia Links\n",
    "\n",
    "https://en.wikipedia.org/wiki/Probability_distribution\n",
    "\n",
    "https://en.wikipedia.org/wiki/Random_variable\n",
    "\n",
    "https://en.wikipedia.org/wiki/Sample_space\n",
    "\n",
    "https://en.wikipedia.org/wiki/Central_tendency\n",
    "\n",
    "https://en.wikipedia.org/wiki/Expected_value\n",
    "\n",
    "https://en.wikipedia.org/wiki/Standard_deviation\n",
    "\n",
    "https://en.wikipedia.org/wiki/Variance\n",
    "\n",
    "https://en.wikipedia.org/wiki/Probability_density_function\n",
    "\n",
    "https://en.wikipedia.org/wiki/Central_limit_theorem\n",
    "\n",
    "https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule\n",
    "\n",
    "https://en.wikipedia.org/wiki/Cumulative_distribution_function\n",
    "\n",
    "https://en.wikipedia.org/wiki/Skewness\n",
    "\n",
    "https://en.wikipedia.org/wiki/Kurtosis"
   ]
  }
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rBUAQxC6DiKhJYlgnImqCBEFAXkklMgrLkVlYjozCMmQUliOj4K+fswrLkVFYjqJyNQxk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\nUKnRImzvVbz81RHEpRbA0li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